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Solution by set Algebra Instead of Venn diagram for following question

Fuzzy Venn diagram regions labeled in ternaryA problem on Venn diagramThree set Venn diagram$A Delta C = B Delta C$, then prove that $A = B$ where $Delta$ is a symmetric difference operation.Simple sample space probability questionIs the set ∅ part of the set UBoolean Algebra Union and Intersectionis this venn diagram of posets, osets and lattices correct?True or False: $A ∩ B = ∅ $ and $B ∩ C = ∅$, then $A ∩ C = ∅$?Venn Diagram tool to help with learning set theory

1

$begingroup$

(P ∩ Q ∩ R) U (P′∩ Q ∩ R)U Q′U R′

I am able to solve the set algebraic equation through Venn diagram and the solution is as under:

set 1 = $(P ∩ Q ∩ R)$ is region 1

set 2 = $(P′∩ Q ∩ R)$ is region 2

set 3 = $Q'$ belongs to regions 4+3+6+8

set 4 = $R'$ belongs to regions 4+7+5+8

and the union of set 1 1 set 2 2 set 3 4,3,6,8 set 4 4,7,5,8

will be 1,2,3,4,5,6,7,8 that is the universal set itself. I am able to get the correct answer but my approach is through Venn diagram. But some where I have found some algebraic approach through some set operation that I am not able to understand. Can somebody please guide me?
Following is the link of the algebraic approach.
Please click here

elementary-set-theory

share|cite|improve this question

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  You can start applying Distributivity to $(P cap Q cap R) cup (P′ cap Q cap R)$ to get $(Q cap R)$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Then apply De Morgan to $(Q′ cup R′)$ to get $(Q cap R)'$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:57
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Now you have : $(Q∩R) cup (Q∩R)'$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:57
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Got it . Thank you @Mauro ALLEGRANZA
  $endgroup$
  – Thinker
  2 days ago
  

  
  
  
  

add a comment | 

1

$begingroup$

(P ∩ Q ∩ R) U (P′∩ Q ∩ R)U Q′U R′

I am able to solve the set algebraic equation through Venn diagram and the solution is as under:

set 1 = $(P ∩ Q ∩ R)$ is region 1

set 2 = $(P′∩ Q ∩ R)$ is region 2

set 3 = $Q'$ belongs to regions 4+3+6+8

set 4 = $R'$ belongs to regions 4+7+5+8

and the union of set 1 1 set 2 2 set 3 4,3,6,8 set 4 4,7,5,8

will be 1,2,3,4,5,6,7,8 that is the universal set itself. I am able to get the correct answer but my approach is through Venn diagram. But some where I have found some algebraic approach through some set operation that I am not able to understand. Can somebody please guide me?
Following is the link of the algebraic approach.
Please click here

elementary-set-theory

share|cite|improve this question

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  You can start applying Distributivity to $(P cap Q cap R) cup (P′ cap Q cap R)$ to get $(Q cap R)$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Then apply De Morgan to $(Q′ cup R′)$ to get $(Q cap R)'$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:57
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Now you have : $(Q∩R) cup (Q∩R)'$.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 12 at 8:57
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Got it . Thank you @Mauro ALLEGRANZA
  $endgroup$
  – Thinker
  2 days ago
  

  
  
  
  

add a comment | 

$begingroup$

(P ∩ Q ∩ R) U (P′∩ Q ∩ R)U Q′U R′

I am able to solve the set algebraic equation through Venn diagram and the solution is as under:

set 1 = $(P ∩ Q ∩ R)$ is region 1

set 2 = $(P′∩ Q ∩ R)$ is region 2

set 3 = $Q'$ belongs to regions 4+3+6+8

set 4 = $R'$ belongs to regions 4+7+5+8

and the union of set 1 1 set 2 2 set 3 4,3,6,8 set 4 4,7,5,8

will be 1,2,3,4,5,6,7,8 that is the universal set itself. I am able to get the correct answer but my approach is through Venn diagram. But some where I have found some algebraic approach through some set operation that I am not able to understand. Can somebody please guide me?
Following is the link of the algebraic approach.
Please click here

elementary-set-theory

share|cite|improve this question

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

$endgroup$

share|cite|improve this question

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

share|cite|improve this question

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

edited Mar 12 at 8:48

Mauro ALLEGRANZA

67.1k449115

asked Mar 12 at 8:22

ThinkerThinker

63

asked Mar 12 at 8:22

ThinkerThinker

63