Question

A union B whole complement =A complement intersection B complement verify​

Answer 1

Step-by-step explanation:

Let U be any universal set and A and B be its two subsets such that :

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

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

Therefore,

$A \cup B = \{ 1, 2, 3, 4, 6, 7, 8\} \: \\ \therefore \: (A \cup B)^{'} = \{ 5\}......(1) \\ now \\ A ^{'} =\{5, 6, 7, 8\} \\ B ^{'} =\{1, 2, 3, 4, \: 5\} \\ \therefore \: A ^{'} \cap B^{'} = \{ 5\}......(2) \\ from \: equations \: (1) \: and \: (2) \: we \: \\ find: \\ (A \cup B)^{'} =A ^{'} \cap B^{'} \: \\ hence \: proved:$

Answer 2

By applying De Morgan’s Law,

(A’ ∩ B’) ∪ (A’ ∩ B)

By distributive law,

A’ ∩ [(B’ ∪ B)]

= A’ ∩ U

= A’