Question

Using
venn diagram, show that
AU(B nC) = (AUB)n(AUC)​

Answer 1

Step-by-step explanation:

let

A={1,2,3,4,5,6}✔✔

B={3,4,5,6}✔✔

C={1,2,3}✔✔

TO PROVE-

AU(B n C)=(AUB)n(AUC)✔✔

PROOF--

LHS

AU(B nC)

AU{3,4,5,6}n{1,2,3}

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

={1,2,3,4,5,6}

=A✔✔

RHS

(AUB)n(AUC)

={1,2,3,4,5,6}n{1,2,3,4,5,6}

={1,2,3,4,5,6}

=A✔✔

THEREFORE, LHS=RHS✔✔

SO, AU(B nC)=(AUB)n(AUC)✔✔

PROVED