Set Theory Practice Solution2





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