Let U = {1, 2, 3, 4, 5, 6}, A = {2,3} and B = {3,4,5).
Find A', B', A' B', A UB and hence show that (AUB)' = A'N B'.
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ANSWER
U = {1,2,3,4,5,6}
A = {2,3}
B = {3,4,5}
A∪B={2,3} ∪ {3,4,5} = {2,3,4,5}
Therefore, (A∪B)
′
= {1,6}
Also, A
′
= {1,4,5,6}
B
′
= {1,2,6}
Therefore, A
′
∩B
′
= {1,4,5,6} ∩ {1,2,6} = {1,6}
Hence, (A∪B)
′
=A
′
∩B
′
.
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