# Infinity And Complements

Probability 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.

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