In this page set theory practice solution2 we are going to see solution of practice questions from the worksheet set theory practice questions1.

**Question 5**

Given A = {a,x,y,r,s}, B = {1,3,5,7,-10},verify the commutative property of set union.

**Solution:**

commutative property of set union

A U B = B U A

A U B = {a,x,y,r,s} U {1,3,5,7,-10}

= {a,x,y,r,s,1,3,5,7,-10} ------ (1)

B U A = {1,3,5,7,-10} U {a,x,y,r,s}

= {a,x,y,r,s,1,3,5,7,-10} ------ (2)

(1) = (2)

**Question 6**

Verify the commutative property of set intersection for A = {l,m,n,o,2,3,4,7} and B = {2,5,3,-2,m,n,o,p}

**Solution:**

commutative property of set intersection

A ⋂ B = B ⋂ A

A ⋂ B = {l,m,n,o,2,3,4,7} ⋂ {2,5,3,-2,m,n,o,p}

= {m,n,o} --- (1)

B ⋂ A = {2,5,3,-2,m,n,o,p} ⋂ {l,m,n,o,2,3,4,7}

= {m,n,o} --- (2)

(1) = (2)

**Question 7**

For A = {x|x is a prime factor of 42}, B ={x|5 < x ≤ 12, x ∈ N} and C = {1,4,5,6} verify A U (B U C) = (A U B) U C.

**Solution:**

A = {x|x is a prime factor of 42}

A = {2,3,7}

B ={x|5 < x ≤ 12, x ∈ N}

B = {6,7,8,9,10,11,12}

C = {1,4,5,6}

L.H.S

A U (B U C)

(B U C) = {6,7,8,9,10,11,12} U {1,4,5,6}

= {1,4,5,6,7,8,9,10,11,12}

A U (B U C) = {2,3,7} U {1,4,5,6,7,8,9,10,11,12}

= {1,2,3,4,5,6,7,8,9,10,11,12} --- (1)

R.H.S

(A U B) U C

(A U B) = {2,3,7} U {6,7,8,9,10,11,12}

= {2,3,6,7,8,9,10,11,12}

(A U B) U C = {2,3,6,7,8,9,10,11,12} U {1,4,5,6}

= {1,2,3,5,6,7,8,9,10,11,12} ----(2)

(1) = (2)

**Question 8**

Given P = {a,b,c,d,e} Q = {a,e,i,o,u} and R ={a,c,e,g}. Verify the associative property of set intersection.

**Solution:**

P ∩ (Q ∩ R) = (P ∩ Q) ∩ R

L.H.S

P ∩ (Q ∩ R)

(Q ∩ R) = {a,e,i,o,u} ∩ {a,c,e,g}

= {a,e}

P ∩ (Q ∩ R) = {a,b,c,d,e} ∩ {a,e}

= {a,e} ---- (1)

R.H.S

(P ∩ Q) ∩ R

(P ∩ Q) = {a,b,c,d,e} ∩ {a,e,i,o,u}

= {a,e}

(P ∩ Q) ∩ R = {a,e} ∩ {a,c,e,g}

= {a,e} ---- (2)

(1) = (2)

Hence proved

set theory practice questions1 set theory practice questions1

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- 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