Is the following argument valid or invalid?

Question

On vacation I'll either go to the beach or I'll swim in the pool.

I went to the beach.

Therefore, I didn't swim in the pool.

Answer 1

This argument is invalid.

In logic, the 'or' connective (also called 'disjunction') is inclusive. This means that if 'X or Y' is true, then it's possible that *both* X and Y are true.

In your example, you suppose that B or P is true, then suppose that B is true. Since 'or' is inclusive, this is perfectly compatible with P being true, too -- so we cannot validly conclude ~P, as your example does.

Answer 2

On vacation I'll either go to the beach or I'll swim in the pool.

I went to the beach.

Therefore, I didn't swim in the pool.

Change your sentence to variables, like the other tutor said.

p v q

p

~q

If P, then Q.

P.

Therefore, Q.

instead, we have not Q

in logic, if you have an OR, as long as one is true, it's ok.

Check with the other answer for more details as well, but this is a Modus Ponens, MP style logical question.