Question

if A = {1,2,3,4,5}, B={2,4,6,8}, and C = {2,3,5,7} then prove that: AU(BUC) =(AUB)C

Answer 1

Answer:

SOLUTION

HERE;

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

B={2, 4, 6, 8}

C={2, 3, 5, 7}

Now;

AU (BUC)={1, 2, 3, 4, 5}U ({2, 4, 6, 8}U {2, 3, 5, 7}

={1, 2, 3, 4, 5}U {2, 3, 2,4, 5, 7, 8} AU(BUC ) ={1, 2, 3, 4, 5, 6, 7, 8}

Again;

(AUB)C=({1, 2, 3, 4, 5}U2, 4, 6, 8})C

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

(AUB)C={1, 2, 3, 4, 5, 6, 7, 8}

Then,

AU(BUC)=(AUB)UC

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

proved