Question

Let A = {x : x ∈ N, x is a multiple of 3} and B = {x : x ∈ N and x is a multiple of 5}. Write $A\cap B$.

Answer 1

A = {x:x ∈ N and x is a multiple of 3.}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,...}
B = {x:x ∈ N and x is a multiple of 5.}
={5, 10, 15, 20, 25, 30, 35, 40, 45,...}
Thus, we have:
$A\cap B$ = {15, 30, 45,...}
= {x:x ∈ N, where x is a multiple of 15.}