## SET THEORY PRACTICE SOLUTION1

Set theory practice solution1 :

Here we are going to see solution of practice questions from the worksheet set theory practice questions1.

Question 1 :

If A ⊂ B,then show that A U B = B (use venn diagram)

Solution :

Since A is the subset of B we have to draw a small circle A inside the large circle B. A U B = B

Question 2 :

If A ⊂ B, then find A ∩ B and A \ B (use venn diagram)

Solution :

Since A is the subset of B we have to draw a small circle A inside the large circle B.

A ∩ B means we have to shade common part of A and B. From this we will get

A ∩ B  =  A Question 3 :

Let P = {a, b, c}, Q = {g, h, x, y} and R = {a, e, f, s}. Find the following

(i) P \ R    (ii)  Q ∩ R        (iii) R \ (P ∩ Q)

Solution :

(i) To find P \ R we have to choose the common elements from both P and R and we have to write remaining elements in P.

P \ R  =  {a, b, c} \ {a, e, f, s}

=  {b, c}

(ii) To find Q ∩ R we have to write the common elements in Q and R.

Q ∩ R  = {g,h,x,y} ∩ {a,e,f,s}

there is no common elements in both Q and R

Q ∩ R  = Ø

(iii) R \ (P ∩ Q)

P ∩ Q = {a,b,c} ∩ {g,h,x,y}

There is no common elements in both P and Q

P ∩ Q = Ø

R \ (P ∩ Q)  =  {a,b,c} \ Ø

=  {a,b,c}

Question 4 :

If A = {4, 6, 7, 8, 9} , B = {2, 4, 6} and C = {1, 2, 3, 4, 5, 6}, then find

(i) A U (B ∩ C)    (ii) A ∩ (B U C)       (iii) A \ (C \ B)

Solution :

(i) A U (B ∩ C)

(B ∩ C) = {2, 4, 6} ∩ {1, 2, 3, 4, 5, 6}

=  {2, 4, 6}

A U (B ∩ C) = {4, 6, 7, 8, 9} U {2, 4, 6}

=  {2, 4, 6, 7, 8, 9}

(ii) A ∩ (B U C)

(B U C) = {2 ,4, 6} U {1, 2, 3, 4, 5, 6}

= {1, 2, 3, 4, 5, 6}

A ∩ (B U C) = {4, 6, 7, 8, 9} ∩ {1, 2, 3, 4, 5, 6}

= {4, 6}

(iii) A \ (C \ B)

C \ B = {1, 2, 3, 4, 5, 6} \ {2, 4, 6}

= {1, 3, 5}

A \ (C \ B) = {4, 6, 7, 8, 9} \ {1, 3, 5}

= {4, 6, 7, 8, 9}

## Related topics

set theory practice solution1 set theory practice solution1

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