Answer to Question #217343 in Discrete Mathematics for Halyufer

Question

Let A be the set of natural numbers multiples of 20 and B the set of natural numbers multiples of 15. Which is the set A ∩ B?

A.natural numbers multiples of 60

B. natural numbers multiples of 5

C. natural numbers multiples of 300

D. natural numbers multiples of 30

Answer 1

$\text{By definition we have the following: } \\ A = \{ 20k \mid k \in \mathbb{N} \} = \{ 20, 40, 60, 80, 100, 120, 140, \dots \} \\ B = \{ 15n \mid n \in \mathbb{N} \} = \{ 15, 30, 45, 60, 75, 90, 105, 120, \ldots \}\\ A \cap B = \{ 60, 120, 180, \ldots \} = \{ 60m \mid m \in \mathbb{N} \}\\ \text{Answer = A. Natural numbers multiples of 60}$