Let A n epsilon Z n 5r for some integer r and B m epsilon

Let A = {n epsilon Z| n = 5r for some integer r} and B = {m epsilon Z| m = 20s for some integer s} Is A SubsetEqual S? Explain. Is B SubsetEqual A? Explain.

Solution

a)

A is set of multiples of 5

B i set of multiples of 20

No. A is not a subset of B

BEcause, 5 is in A but 5 is not in B

b)

YEs.

Let, m=20s be in B

Then, m=20s=5*(4s)

Hence, m is in A

Hence proved