Question

if U={4,7,8,10,11,12,15,16},A={7,8,11,12} and B={4,8,12,15} then verify De Morgan's for complementation​

Answer 1

Answer:

1.(A∪B)'= A' ∩ B'

2. (A∩B)'= A'∪B'

Explanation:

If U={4,7,8,10,11,12,15,16},A={7,8,11,12} and B={4,8,12,15} then verify De Morgan's for complementation​

Demorgan's law for complementation:

1.(A∪B)'= A' ∩ B'

2. (A∩B)'= A'∪B'

Verification:

1.

A∪B = {4,7,8,11,12,15}

(A∪B)' = {10,16}..........(1)

A'={4,10,15,16}

B'={7,10,11,16}

A'∩B'={10,16}...............(2)

From (1) and (2)

(A∪B)'= A'∩B'

2.

A∩B={8,12}

(A∩B)'={4,7,10,11,15,16}.............(3)

A'={4,10,15,16}

B'={7,10,11,16}

A'∪B'={4,7,10,11,15,16}...............(4)

From (3) and (4)

(A∩B)'= A'∪B'