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 moragans law is : ( A U B)' = A' intersection B '

U = { 4, 5, 6, 7}

A = { 4,5 }

B = { 5 ,6 ,7 }

so A U B = { 4, 5} U { 5 , 6 ,7 }

= { 4 , 6 , 7 }

( A U B )' = { 5 }

LHS = { 5}

A = { 4,5}

U = { 4,5,6,7}

so A' = n(U) intersection n(A)

= { 4,5 }

similarly:

B ' = { 5}

so A' intersection B'

= {4,5} intersection {5 }

RHS = { 5 }

SO LHS = RHS

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