Question

A={0,2,4,6,8} B={x:x is a prime number and x<11} and C={x:x€N and 5<x<9} then verify that AU(BnC) = (AUB)n(AUC)
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Answer 1

Answer:

A={0,2,4,6,8}

B={2,3,5,7}

C={6,7,8}

L.H.S

AU(BnC) ==> BnC = {7}

AU(BnC)={0,2,4,6,7,8} ------(1)

R.H.S

(AUB)n(AUC) ==> AUB = {0,2,3,4,5,6,7,8}

AUC = {0,2,4,6,7,8}

(AUB)n(AUC)={0,2,4,6,7,8} ------(2)

from (1) and (2)

we got Lhs = Rhs

==> AU(BnC)=(AUB)n(AUC)

:• hence proved