Exercise 10.

Consider the statement, “If a number is triangular or square, then it is not prime”

  1. Make a truth table for the statement \((T \vee S) \imp \neg P\text{.}\)

  2. If you believed the statement was false, what properties would a counterexample need to possess? Explain by referencing your truth table.

  3. If the statement were true, what could you conclude about the number 5657, which is definitely prime? Again, explain using the truth table.

Hint.
in-context