Which one is true?

Logic Level 4

Which of the following statements are true?

  1. If \(n\) is a prime number and a square number, then \(n\) is a triangular number.
  2. If \(n\) is a prime number and a square number, then \(n\) is not a triangular number.

Assumption:

Assume classical logic, in particular the law of excluded middle: \(p \vee \neg p\) is a tautology.

Notes:

  • A prime number is a positive integer greater than \(1\) that is only divisible by \(1\) and itself.
  • A square number is an integer that can be expressed in the form \(n^2\) for some integer \(n\).
  • A triangular number is an integer that can be expressed in the form \(\frac{n(n+1)}{2}\) for some integer \(n\).
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