Question

If A={x:XEN ,x<7) B={x: x is prime, x<8} and

C={x: XEN, x is odd and x<10) verify that

i)A U(BnC) = (AUB)n(AUC).

(ii) An (BUC) = (AB)(Ang)​

Answer 1

Answer:

i)

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

B={2, 3,5,7}

C={1, 3,5,7,9}

L. H. S, AU(BnC) ={1, 2,3,4,5,6}U[{2, 3,5,7}n{1, 3,5,7,9}]

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

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

R. H. S, (AUB) n(AUC) =[{1, 2,3,4,5,6}U{2, 3,5,7}]n[{1, 2,3,4,5,6}U{1, 3,5,7,9}]

={1, 2,3,4,5,6,7}n{1, 2,3,4,5,6,7,9}

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

Therefore, L. H. S=R.H.S

ii) Same methods apply in question number (ii)