Question

If U = {1, 2, 3, 4, 5), A = {1, 2, 3} and B = {3, 4, 5} then verify:
i)(A U B)' = A' n B'
ii)(A n B)' = A' U B'
Note: These two relations are called De-Morgan's Laws.​

Answer 1

Answer:

I)(A U B)={1,2,3,4,5}

(A U B)'={phi}

l.h.s

A'={4,5}

B'={1,2}

A' n B'={phi}

r.h.s

therefore l.h.s=r.h.s

hence proved

ii)(A n B)={3}

(A n B)'={1,2,4,5}

l.h.s

A' U B'={1,2,4,5}

r.h.s

hence proved l.h.s=r.h.s

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