# Which statement about the following argument is true? If an animal is a koala, then it is a marsupial. If an animal is a marsupial, then it carries its young in a pouch. Therefore, if an animal is a koala, then it carries its young in a pouch.

## $$  A. The argument is valid by the Law of Syllogism. B. The argument is valid by the Law of Detachment. C. The argument is invalid. D. The argument is valid but does not follow the Law of Syllogism or the Law of Detachment.

Oct 21, 2016

A. The argument is valid by the Law of Syllogism

#### Explanation:

The law of syllogism is a form of deductive reasoning which allows us to directly relate propositions connected by an intermediate proposition.

The general form is that if $P , Q , R$ are propositions, and we are given the following implications:

$P \to Q$ (The truth of $P$ implies the truth of $Q$)

$Q \to R$ (The truth of $Q$ implies the truth of $R$)

then we can deduce that $P \to R$ (the truth of $P$ implies the truth of $R$).

In this case, let $P$ be the proposition that an animal is a koala, $Q$ be the statement that an animal is a marsupial, and $R$ be the statement that an animal carries its young in a pouch.

From the question, we are given:

"If an animal is a koala, then it is a marsupial."
i.e. If $P$ then $Q$
i.e. $P \to Q$

"If an animal is a marsupial, then it carries its young in a pouch."
i.e. If $Q$ then $R$.
i.e. $Q \to R$

Applying the law of syllogism, we are able to deduce that

$P \to R$
i.e. If $P$ then $R$.
i.e. If an animal is a koala, then it carries its young in a pouch.

This matches the final statement of the question.