Question

A ={1,2,3,4} and B={2,4,6,8} ,C={1,3,5}, show that AU(B∩C) = (A∪B) ∩ (A∪C)?​

Answer 1

Answer:

LHS = {1,2,3,4}

RHS = {1,2,3,4}

.: LHS = RHS

Step-by-step explanation:

LHS = AU(B∩C)

= {1,2,3,4} U [{2,4,6,8} ∩ {1,3,5}]

= {1,2,3,4} U { }

LHS = {1,2,3,4}

RHS = (A∪B) ∩ (A∪C)

= [ {1,2,3,4} U {2,4,6,8} ] ∩ [ {1,2,3,4} U {1,3,5} ]

= { 1,2,3,4,6,8} ∩ {1,2,3,4,5}

RHS = {1,2,3,4}