Question

A={1,2,3,4,5},B={3,4,5,6} and C={5,6,7,8} and, Show that Au(BuC)=(AuB)uC

Answer 1

$<b>$Given : A={1,2,3,4,5},B={3,4,5,6} and C={5,6,7,8}

To prove : Au(BuC)=(AuB)uC

Proof:
LHS
= Au(BuC)

Find BuC
BuC = {3,4,5,6}u{5,6,7,8}
BuC={3,4,5,6,7,8}

Au(BuC) = {1,2,3,4,5}u{3,4,5,6,7,8} ={1,2,3,4,5,6,7,8}✓✓✓✓ --------(1)

RHS
= (AuB)uC

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

(AuB)uC
= {1,2,3,4,5,6} u {5,6,7,8}
{1,2,3,4,5,6,7,8}✓✓✓✓ --------(2)

(1) = (2)
So LHS = RHS

Hence proved
✓✓✓✌