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)