Question

if A={1, 2,3,4,5,6,7};B{2, 4,6,8};C{4, 5,6,7}.verify A n(b u c) = ( A n B) U (A n C).​

Answer 1

Answer:

Given,

A = {1,2,3,4,5,6,7}

B = {2,4,6,8}

C = {4,5,6,7}

A n(B u C)

(B u C)= {2,4,6,8} u {4,5,6,7}

= {2,4,5,6,7,8}

A n(B u C) = {1,2,3,4,5,6,7} n {2,4,5,6,7,8}

= {2,4,5,6,7} _ (1)...

(A n B) = {1,2,3,4,5,6,7} n {2,4,6,8}

= {2,4,6}

(A n C) = {1,2,3,4,5,6,7} n {4,5,6,7}

= {4,5,6,7}

(A n B) u (A n C) = {2,4,6} u {4,5,6,7}

= {2,4,5,6,7} _ (2)...

from (1) and (2) ,A n(B u C) = (A n B) u (A n C) is verified.

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