Infinity And Complements

Probability Level 2

Suppose XNX \subseteq \mathbb{N}

Let AA be the statement that XX contains finitely many elements.

Let BB be the statement that the complement of XX, say X=NXX'= \mathbb{N} \setminus X contains infinitely many elements.

Which of the following implications is/are true?

(1): A    BA \implies B.
(2): B    AB \implies A.

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

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