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Discrete Mathematics - Set Theory

For each natural number nn, let

An={ k∈N∣k≥n}.A_n = \{\, k \in \mathbb{N} \mid k \ge n \}.

Determine if the following statements are true or false. Justify each conclusion.

  1. For all j,k∈Nj, k \in \mathbb{N}, if j≠kj \neq k, then Aj∩Ak≠∅A_j \cap A_k \neq \varnothing.

  2. ⋂k∈NAk=∅.\displaystyle \bigcap_{k \in \mathbb{N}} A_k = \varnothing.

Probability

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