# Infinity And Complements

**Discrete Mathematics**Level 2

Suppose \(X \subseteq \mathbb{N}\)

Let \(A\) be the statement that \(X\) contains **finitely** many elements.

Let \(B\) be the statement that the complement of \(X\), say \(X'= \mathbb{N} \setminus X\) contains **infinitely** many elements.

Which of the following implications is/are true?

**(1)**: \(A \implies B\).

**(2)**: \(B \implies A\).

**Notation**: \(\mathbb N \) denotes the set of natural numbers.