Express each of these sentences in terms of Q(x, y), quantifiers, and logical connectives [closed]Express each of these sentences in terms of $Q(x, y)$, quantifiers, and logical connectives,Difference between these two logical expressionHow to express the following statement with Quantifiers and PredicatesNested Quantifiers (And vs Implies)Nested Quantifiers Implications or Logical And?Use quantifiers to express each of these statementsQuestions dealing with nested quantifiersHow to use quantifiers to express these statementsWriting english statement into predicate logic using quantifiers.Conversion of English statement to Logic Expression Using quantifiers
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Express each of these sentences in terms of Q(x, y), quantifiers, and logical connectives [closed]
Express each of these sentences in terms of $Q(x, y)$, quantifiers, and logical connectives,Difference between these two logical expressionHow to express the following statement with Quantifiers and PredicatesNested Quantifiers (And vs Implies)Nested Quantifiers Implications or Logical And?Use quantifiers to express each of these statementsQuestions dealing with nested quantifiersHow to use quantifiers to express these statementsWriting english statement into predicate logic using quantifiers.Conversion of English statement to Logic Expression Using quantifiers
$begingroup$
Let Q(x, y) be the statement “student x has been a contestant
on quiz show y.” Express each of these sentences
in terms of Q(x, y), quantifiers, and logical connectives,
where the domain for x consists of all students at your
school and for y consists of all quiz shows on television.
a) There is a student at your school who has been a contestant
on a television quiz show.
b) No student at your school has ever been a contestant
on a television quiz show.
c) There is a student at your school who has been a contestant
on Jeopardy and on Wheel of Fortune.
d) Every television quiz show has had a student from
your school as a contestant.
e) At least two students from your school have been contestants
on Jeopardy.
(Reference: Discrete Mathematics (7th Edition) Kenneth H. Rosen, Exercise-1.5 Question No.-8)
I am not able to solve this question. What the approach to solve this question? Please Explain
logic predicate-logic quantifiers logic-translation
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
$endgroup$
closed as off-topic by Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel Mar 17 at 2:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel
add a comment |
$begingroup$
Let Q(x, y) be the statement “student x has been a contestant
on quiz show y.” Express each of these sentences
in terms of Q(x, y), quantifiers, and logical connectives,
where the domain for x consists of all students at your
school and for y consists of all quiz shows on television.
a) There is a student at your school who has been a contestant
on a television quiz show.
b) No student at your school has ever been a contestant
on a television quiz show.
c) There is a student at your school who has been a contestant
on Jeopardy and on Wheel of Fortune.
d) Every television quiz show has had a student from
your school as a contestant.
e) At least two students from your school have been contestants
on Jeopardy.
(Reference: Discrete Mathematics (7th Edition) Kenneth H. Rosen, Exercise-1.5 Question No.-8)
I am not able to solve this question. What the approach to solve this question? Please Explain
logic predicate-logic quantifiers logic-translation
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
$endgroup$
closed as off-topic by Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel Mar 17 at 2:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel
add a comment |
$begingroup$
Let Q(x, y) be the statement “student x has been a contestant
on quiz show y.” Express each of these sentences
in terms of Q(x, y), quantifiers, and logical connectives,
where the domain for x consists of all students at your
school and for y consists of all quiz shows on television.
a) There is a student at your school who has been a contestant
on a television quiz show.
b) No student at your school has ever been a contestant
on a television quiz show.
c) There is a student at your school who has been a contestant
on Jeopardy and on Wheel of Fortune.
d) Every television quiz show has had a student from
your school as a contestant.
e) At least two students from your school have been contestants
on Jeopardy.
(Reference: Discrete Mathematics (7th Edition) Kenneth H. Rosen, Exercise-1.5 Question No.-8)
I am not able to solve this question. What the approach to solve this question? Please Explain
logic predicate-logic quantifiers logic-translation
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
$endgroup$
Let Q(x, y) be the statement “student x has been a contestant
on quiz show y.” Express each of these sentences
in terms of Q(x, y), quantifiers, and logical connectives,
where the domain for x consists of all students at your
school and for y consists of all quiz shows on television.
a) There is a student at your school who has been a contestant
on a television quiz show.
b) No student at your school has ever been a contestant
on a television quiz show.
c) There is a student at your school who has been a contestant
on Jeopardy and on Wheel of Fortune.
d) Every television quiz show has had a student from
your school as a contestant.
e) At least two students from your school have been contestants
on Jeopardy.
(Reference: Discrete Mathematics (7th Edition) Kenneth H. Rosen, Exercise-1.5 Question No.-8)
I am not able to solve this question. What the approach to solve this question? Please Explain
logic predicate-logic quantifiers logic-translation
logic predicate-logic quantifiers logic-translation
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
edited Mar 15 at 16:57
Taroccoesbrocco
5,64271840
5,64271840
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
asked Mar 3 at 5:31
Sumit RanjanSumit Ranjan
368
368
closed as off-topic by Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel Mar 17 at 2:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel
closed as off-topic by Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel Mar 17 at 2:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Vinyl_cape_jawa, Shaun, José Carlos Santos, Parcly Taxel
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I hope that you are clear with the quantifiers and their use. I will show in this answer how to use them together with the logical connectives in order solve the problem.
a) Given statement is: "There is a student in your school who has been a contestant in a television quiz show". First, identify the set. Clearly it is the set of students in the school. Name that set $S$. What does the statement say? It says "there is a student", which in terms of quantifiers means $exists x in S$. What property does this $x$ hold? It has contested in a television quiz show. So, for us, $y = $ television quiz show. Now, we combine all this information in a single logic statement involving quantifiers:-
$$exists x in S left( Q left( x, text television quiz show right) right)$$
b) Given statement is: "No student at your school has ever been a contestant on a television quiz show". This can also be said as, "Given any student in your school, the student has not been on a television quiz show". So, the quantifier being used is $forall$. What property does every student hold? It is that the student has not participated in television quiz show. If $Q left( x, text television quiz show right)$ means that $x$ has participated in the show, then $neg Q left( x, text television quiz show right)$ means that $x$ has not participated. Hence, the given statement in form of logical connectives is
$$forall x in S left( neg Q left( x, text television quiz show right) right)$$
c) This goes same as a) with two television shows thereby making the logical statement as:
$$exists x in S left( Q left( x, textJeopardy right) wedge Q left( x, textWheel of Fortune right) right)$$
d) Given statement: "Every television show has had a student from your school as a contestant." Here, two sets are involved: The set of all television shows, say $T$, and second, the set of all students of your school, say $S$. Now, first we pick "any" television show, i.e., $forall t in T$. What property does this $t$ hold? It holds that one student from your school, i.e., $exists s in S$ has participated in it, i.e., $Q left( s, t right)$ holds true. Hence, the given statement in terms of quantifiers is given as
$$forall t in T left( exists s in S left( Q left( s, t right) right) right)$$
e) Given statement is: "At least two students have been contestants on Jeopardy". Since the statement says, there are "at least two" students, we use the quantifier $exists x in S$ and $exists y in S$ with an additional property that $x neq y$ (so that at least two holds in general). The property that both the students hold is that for both of them $Q left( x, textJeopardy right)$ and $Q left( y, textJeopardy right)$ holds true. So, in terms of quantifiers, we write:
$$exists x in S wedge exists y in S left( x neq y wedge Q left( x, textJeopardy right) wedge Q left( y, textJeopardy right) right)$$
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I hope that you are clear with the quantifiers and their use. I will show in this answer how to use them together with the logical connectives in order solve the problem.
a) Given statement is: "There is a student in your school who has been a contestant in a television quiz show". First, identify the set. Clearly it is the set of students in the school. Name that set $S$. What does the statement say? It says "there is a student", which in terms of quantifiers means $exists x in S$. What property does this $x$ hold? It has contested in a television quiz show. So, for us, $y = $ television quiz show. Now, we combine all this information in a single logic statement involving quantifiers:-
$$exists x in S left( Q left( x, text television quiz show right) right)$$
b) Given statement is: "No student at your school has ever been a contestant on a television quiz show". This can also be said as, "Given any student in your school, the student has not been on a television quiz show". So, the quantifier being used is $forall$. What property does every student hold? It is that the student has not participated in television quiz show. If $Q left( x, text television quiz show right)$ means that $x$ has participated in the show, then $neg Q left( x, text television quiz show right)$ means that $x$ has not participated. Hence, the given statement in form of logical connectives is
$$forall x in S left( neg Q left( x, text television quiz show right) right)$$
c) This goes same as a) with two television shows thereby making the logical statement as:
$$exists x in S left( Q left( x, textJeopardy right) wedge Q left( x, textWheel of Fortune right) right)$$
d) Given statement: "Every television show has had a student from your school as a contestant." Here, two sets are involved: The set of all television shows, say $T$, and second, the set of all students of your school, say $S$. Now, first we pick "any" television show, i.e., $forall t in T$. What property does this $t$ hold? It holds that one student from your school, i.e., $exists s in S$ has participated in it, i.e., $Q left( s, t right)$ holds true. Hence, the given statement in terms of quantifiers is given as
$$forall t in T left( exists s in S left( Q left( s, t right) right) right)$$
e) Given statement is: "At least two students have been contestants on Jeopardy". Since the statement says, there are "at least two" students, we use the quantifier $exists x in S$ and $exists y in S$ with an additional property that $x neq y$ (so that at least two holds in general). The property that both the students hold is that for both of them $Q left( x, textJeopardy right)$ and $Q left( y, textJeopardy right)$ holds true. So, in terms of quantifiers, we write:
$$exists x in S wedge exists y in S left( x neq y wedge Q left( x, textJeopardy right) wedge Q left( y, textJeopardy right) right)$$
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
$endgroup$
add a comment |
$begingroup$
I hope that you are clear with the quantifiers and their use. I will show in this answer how to use them together with the logical connectives in order solve the problem.
a) Given statement is: "There is a student in your school who has been a contestant in a television quiz show". First, identify the set. Clearly it is the set of students in the school. Name that set $S$. What does the statement say? It says "there is a student", which in terms of quantifiers means $exists x in S$. What property does this $x$ hold? It has contested in a television quiz show. So, for us, $y = $ television quiz show. Now, we combine all this information in a single logic statement involving quantifiers:-
$$exists x in S left( Q left( x, text television quiz show right) right)$$
b) Given statement is: "No student at your school has ever been a contestant on a television quiz show". This can also be said as, "Given any student in your school, the student has not been on a television quiz show". So, the quantifier being used is $forall$. What property does every student hold? It is that the student has not participated in television quiz show. If $Q left( x, text television quiz show right)$ means that $x$ has participated in the show, then $neg Q left( x, text television quiz show right)$ means that $x$ has not participated. Hence, the given statement in form of logical connectives is
$$forall x in S left( neg Q left( x, text television quiz show right) right)$$
c) This goes same as a) with two television shows thereby making the logical statement as:
$$exists x in S left( Q left( x, textJeopardy right) wedge Q left( x, textWheel of Fortune right) right)$$
d) Given statement: "Every television show has had a student from your school as a contestant." Here, two sets are involved: The set of all television shows, say $T$, and second, the set of all students of your school, say $S$. Now, first we pick "any" television show, i.e., $forall t in T$. What property does this $t$ hold? It holds that one student from your school, i.e., $exists s in S$ has participated in it, i.e., $Q left( s, t right)$ holds true. Hence, the given statement in terms of quantifiers is given as
$$forall t in T left( exists s in S left( Q left( s, t right) right) right)$$
e) Given statement is: "At least two students have been contestants on Jeopardy". Since the statement says, there are "at least two" students, we use the quantifier $exists x in S$ and $exists y in S$ with an additional property that $x neq y$ (so that at least two holds in general). The property that both the students hold is that for both of them $Q left( x, textJeopardy right)$ and $Q left( y, textJeopardy right)$ holds true. So, in terms of quantifiers, we write:
$$exists x in S wedge exists y in S left( x neq y wedge Q left( x, textJeopardy right) wedge Q left( y, textJeopardy right) right)$$
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
$endgroup$
add a comment |
$begingroup$
I hope that you are clear with the quantifiers and their use. I will show in this answer how to use them together with the logical connectives in order solve the problem.
a) Given statement is: "There is a student in your school who has been a contestant in a television quiz show". First, identify the set. Clearly it is the set of students in the school. Name that set $S$. What does the statement say? It says "there is a student", which in terms of quantifiers means $exists x in S$. What property does this $x$ hold? It has contested in a television quiz show. So, for us, $y = $ television quiz show. Now, we combine all this information in a single logic statement involving quantifiers:-
$$exists x in S left( Q left( x, text television quiz show right) right)$$
b) Given statement is: "No student at your school has ever been a contestant on a television quiz show". This can also be said as, "Given any student in your school, the student has not been on a television quiz show". So, the quantifier being used is $forall$. What property does every student hold? It is that the student has not participated in television quiz show. If $Q left( x, text television quiz show right)$ means that $x$ has participated in the show, then $neg Q left( x, text television quiz show right)$ means that $x$ has not participated. Hence, the given statement in form of logical connectives is
$$forall x in S left( neg Q left( x, text television quiz show right) right)$$
c) This goes same as a) with two television shows thereby making the logical statement as:
$$exists x in S left( Q left( x, textJeopardy right) wedge Q left( x, textWheel of Fortune right) right)$$
d) Given statement: "Every television show has had a student from your school as a contestant." Here, two sets are involved: The set of all television shows, say $T$, and second, the set of all students of your school, say $S$. Now, first we pick "any" television show, i.e., $forall t in T$. What property does this $t$ hold? It holds that one student from your school, i.e., $exists s in S$ has participated in it, i.e., $Q left( s, t right)$ holds true. Hence, the given statement in terms of quantifiers is given as
$$forall t in T left( exists s in S left( Q left( s, t right) right) right)$$
e) Given statement is: "At least two students have been contestants on Jeopardy". Since the statement says, there are "at least two" students, we use the quantifier $exists x in S$ and $exists y in S$ with an additional property that $x neq y$ (so that at least two holds in general). The property that both the students hold is that for both of them $Q left( x, textJeopardy right)$ and $Q left( y, textJeopardy right)$ holds true. So, in terms of quantifiers, we write:
$$exists x in S wedge exists y in S left( x neq y wedge Q left( x, textJeopardy right) wedge Q left( y, textJeopardy right) right)$$
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
$endgroup$
I hope that you are clear with the quantifiers and their use. I will show in this answer how to use them together with the logical connectives in order solve the problem.
a) Given statement is: "There is a student in your school who has been a contestant in a television quiz show". First, identify the set. Clearly it is the set of students in the school. Name that set $S$. What does the statement say? It says "there is a student", which in terms of quantifiers means $exists x in S$. What property does this $x$ hold? It has contested in a television quiz show. So, for us, $y = $ television quiz show. Now, we combine all this information in a single logic statement involving quantifiers:-
$$exists x in S left( Q left( x, text television quiz show right) right)$$
b) Given statement is: "No student at your school has ever been a contestant on a television quiz show". This can also be said as, "Given any student in your school, the student has not been on a television quiz show". So, the quantifier being used is $forall$. What property does every student hold? It is that the student has not participated in television quiz show. If $Q left( x, text television quiz show right)$ means that $x$ has participated in the show, then $neg Q left( x, text television quiz show right)$ means that $x$ has not participated. Hence, the given statement in form of logical connectives is
$$forall x in S left( neg Q left( x, text television quiz show right) right)$$
c) This goes same as a) with two television shows thereby making the logical statement as:
$$exists x in S left( Q left( x, textJeopardy right) wedge Q left( x, textWheel of Fortune right) right)$$
d) Given statement: "Every television show has had a student from your school as a contestant." Here, two sets are involved: The set of all television shows, say $T$, and second, the set of all students of your school, say $S$. Now, first we pick "any" television show, i.e., $forall t in T$. What property does this $t$ hold? It holds that one student from your school, i.e., $exists s in S$ has participated in it, i.e., $Q left( s, t right)$ holds true. Hence, the given statement in terms of quantifiers is given as
$$forall t in T left( exists s in S left( Q left( s, t right) right) right)$$
e) Given statement is: "At least two students have been contestants on Jeopardy". Since the statement says, there are "at least two" students, we use the quantifier $exists x in S$ and $exists y in S$ with an additional property that $x neq y$ (so that at least two holds in general). The property that both the students hold is that for both of them $Q left( x, textJeopardy right)$ and $Q left( y, textJeopardy right)$ holds true. So, in terms of quantifiers, we write:
$$exists x in S wedge exists y in S left( x neq y wedge Q left( x, textJeopardy right) wedge Q left( y, textJeopardy right) right)$$
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
answered Mar 3 at 5:47
Aniruddha DeshmukhAniruddha Deshmukh
1,156419
1,156419
add a comment |
add a comment |
