Which one is true?

Logic Level 4

Which of the following statements are true?

  1. If nn is a prime number and a square number, then nn is a triangular number.
  2. If nn is a prime number and a square number, then nn is not a triangular number.

Assumption:

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

Notes:

  • A prime number is a positive integer greater than 11 that is only divisible by 11 and itself.
  • A square number is an integer that can be expressed in the form n2n^2 for some integer nn.
  • A triangular number is an integer that can be expressed in the form n(n+1)2\frac{n(n+1)}{2} for some integer nn.
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