Question

let U = {4, 5, 6, 7}, A = {4, 5} and B = {5, 6, 7}.Verify the De Morgan's laws for A and B.​

Answer 1

★De Morgan's laws

1. ( A or B )'= A' and B'

2. ( A and B)' = A' or B'

Now the given sets in the question.

U ={4,5,6,7}

A ={4,5}

B ={5,6,7}

We shall prove Law 1:

L.H.S

A or B = {4,5,6,7}

(A or B)' = { }

R.H.S

A' = {6,7}

B'={4}

A' and B'={}

★Hence law 1 is proved.

★Similarly we can prove Law 2