Question

If A = {2, 3, 5, 7, 8}, B = {1, 5, 9} and A' = {1, 4, 6, 9), verify that
(i) (A U B)' = A' N B'
​

Answer 1

Step-by-step explanation:

let the universal set be U

A = {2,3,5,7,8}

B ={1,5,9}

A' = { 1,4,6,9}

here, we know that A u A' = U

= {2,3,5,7,8} u {1,4,6,9}

= { 1,2,3,4,5,6,7,8,9}

B' = U - B

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

= {2,3,4,6,7,8}

(A u B) = {2,3,5,7,8} u{1,5,9}={1,2,3,5,7,8,9}

(i) LHS = (AuB)'

=U-(AuB)

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

={4,6}

RHS = A'nB'

= {1,4,6,9} n {2,3,4,6,7,8,}

={4,6,}

LHS = RHS (proved)