**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}

set theory practice solution1 set theory practice solution1

- Definition
- Representation of Set
- Types of set
- Disjoint sets
- Power Set
- Operations on Sets
- Laws on set operations
- More Laws
- Venn diagrams
- Set word problems
- Relations and functions

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