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)