Question

If A={1,2,3,4},B={2,4,5,6},C={1,3,4,6,8},Verify (1) An(BUC) =(AnB)U(AnC),(2) An(BUC)=(AnB)U(AUC)​

Answer 1

Step-by-step explanation:

(1) An(BUC)=(AnB)U(AnC)

An(BUC)= {1,2,3,4}

(AnB)= {2,4}

(AnC)= {1,3,4}

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

{1,2,3,4} = {1,2,3,4} hence, An(BUC)=(AnB)U(AnC)

(2) An(BUC)=(AnB)U(AUC)

Note:( everything is mentioned in 1st setion except AUC)

(AUC)= {1,2,3,4,6,8}

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

{1,2,3,4}={1,2,3,4,6,8}

hence, An(BUC) is not = (AnB)U(AUC)