Question

(1) Given P = {1,2,3,4,5), B = {3,4,5,6) and C = {4,5,6,7,8). Show that A U (BUC)=(AUB) UC​

Answer 1

Step-by-step explanation:

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

L.H.S = (AuB)uC

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

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

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

R.H.S = Au(BuC)

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

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

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

Answer 2

Answer:

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Step-by-step explanation:

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