Given € = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, set P = {1, 2, 4, 6, 8, 10} and set Q = {2, 3, 4, 5, 6, 7, 9, 12). Draw Venn Diagrams for each of the following and list the elements of the sets:
i. (P ٮ Q)'
ii. [(P ٮ Q) ∩ (P ∩ Q)] ٮ (P ٮ Q)'
please help me to get step by step and venn diagram
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Answer:
A={1,2,5,7}
B={3,4,5,6}
(A∪B)
′
=U−(A∪B)
={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}
=ϕ
A
′
∩B
′
=(U−A)n(U−B)
={3,4,6}n{1,2,7}
=ϕ
Hence (A∪B)
′
=A
′
∩B
′
.
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