Question

4) If U = {1,2,3,4,5,6,7,8,9,10), where U denotes the universal set,
A = {1,3,5,7) and B = {1,2,3,4,5). Verify that (An B)' = A'UB'

where ' denotes the complement.​

Answer 1

Step-by-step explanation:

(A∩B)'=A'∪B'

Take L.H.S

(A∩B)'=U-A∩B

A∩B={1,3,5,7}∩{1,2,3,4,5}

A∩B={1,3,5}

U-A∩B={1,2,3,4,5,6,7,8,9,10}-{1,3,5}

(A∩B)'={2,4,6,7,8,9,10}

Take R.H.S

A'∪B'

A'=U-A

U-A={1,2,3,4,5,6,7,8,9,10}-{1,3,5,7}

A'={2,4,6,8,9,10}

B'=U-B

U-B={1,2,3,4,5,6,7,8,9,10}-{1,2,3,4,5}

B'={6,7,8,9,10}

A'∪B'={2,4,6,8,9,10}∪{6,7,8,9,10}

A'∪B'={2,4,6,7,8,9,10}

L.H.S=R.H.S

Hence Proved