Question

let U={1,2,3,4,5,6,7,8},A={2,4,6,8}and B={2,4,8}.verify (A U B)'=A' n B'

Answer 1

♠ ANSWER :

U={1,2,3,4,5,6,7,8},A={2,4,6,8}and B={2,4,8}

(A ∪ B )' = U - ( A ∪ B )

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

= { 1, 3, 5, 7 }

A' ∩ B' = ( U - A ) ∩ ( U - B )

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

= { 1,3,5,7 } ∩ { 1,3,5,6,7 }

= { 1,3,5,7 }

⏺️(A ∪ B )' = A' ∩ B' .

✔️ PROVED.