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Find the minimal and maximal elements of $P^*$?

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1

$begingroup$

Consider the set $1, 2, 3, 4$ and let $P^*:=P(1, 2, 3, 4)-emptyset$ be the set of all subsets of $1, 2, 3, 4$ excepting $emptyset$. Then $P^*$ is ordered via inclusion as follows:

$$Aleq BLeftrightarrow Asubset B.$$

I'm supposed to find the minimal and maximal elements with respect to that order. Can anyone help me?

I believe the minimal elements are the unitary sets $1, 2, 3$ and $4$ and the unique maximal element is $1, 2, 3, 4$. Am I right?

abstract-algebra order-theory

share|cite|improve this question

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's right.
  $endgroup$
  – Théophile
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks a lot =)
  $endgroup$
  – PtF
  yesterday
  

  
  
  
  

add a comment | 

1

$begingroup$

Consider the set $1, 2, 3, 4$ and let $P^*:=P(1, 2, 3, 4)-emptyset$ be the set of all subsets of $1, 2, 3, 4$ excepting $emptyset$. Then $P^*$ is ordered via inclusion as follows:

$$Aleq BLeftrightarrow Asubset B.$$

I'm supposed to find the minimal and maximal elements with respect to that order. Can anyone help me?

I believe the minimal elements are the unitary sets $1, 2, 3$ and $4$ and the unique maximal element is $1, 2, 3, 4$. Am I right?

abstract-algebra order-theory

share|cite|improve this question

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's right.
  $endgroup$
  – Théophile
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks a lot =)
  $endgroup$
  – PtF
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

Consider the set $1, 2, 3, 4$ and let $P^*:=P(1, 2, 3, 4)-emptyset$ be the set of all subsets of $1, 2, 3, 4$ excepting $emptyset$. Then $P^*$ is ordered via inclusion as follows:

$$Aleq BLeftrightarrow Asubset B.$$

I'm supposed to find the minimal and maximal elements with respect to that order. Can anyone help me?

I believe the minimal elements are the unitary sets $1, 2, 3$ and $4$ and the unique maximal element is $1, 2, 3, 4$. Am I right?

abstract-algebra order-theory

share|cite|improve this question

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

$endgroup$

share|cite|improve this question

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

share|cite|improve this question

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

edited yesterday

user26857

39.3k124183

edited yesterday

user26857

39.3k124183

asked yesterday

PtFPtF

4,04821734

asked yesterday

PtFPtF

4,04821734