# 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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