Question

Determine whether the following argument is valid or not. (Let the universe consist of all birds currently living on Earth.) If it is valid provide a formal inference with steps and reasons. If it is not, explain why.

"All parrots like fruit"

"My pet bird is not a parrot."

Therefore my pet bird does like fruit.

Answer 1

Here since we have statement,

All parrot like fruit.

We can write,

1. Parrot (x) -> LikeFruit(x) where x is some constant using universal instantistion.

2. ~Parrot(MyPet) ..... My pet is not a parrot.

Therefore since the premise in the implication,

Parrot(x) -> LikeFruit (x) is False, we cannot conclude anything about the conclusion.

So the given statement is invalid.

If premise would have been true in the implication: Parrot (x) -> LikeFruit (x), then we could have proved that conclusion is True using modus ponens.

So the conclusion is invalid here.

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