Posted by **kozy** on Sunday, May 22, 2011 at 11:50pm.

Determine if the argument is valid or invalid. Give a reason to justify answer.

If it is cold, then you need a coat.

You do not need a coat.

It is not cold.

(Points : 2)

Valid by the law of detachment

Valid by the law of contraposition

Invalid by fallacy of the converse

Invalid by fallacy of the inverse

Valid by the law of syllogism

Valid by disjunctive syllogism

- math -
**MathMate**, Monday, May 23, 2011 at 9:08am
Let

P: "it is cold"

Q: "you need a coat"

The first statement is therefore

P → Q

The second part has been written in two separate statements, ¬Q, ¬P.

If we can *assume* it to be related as "It is not cold, therefore you do not need a coat", or

¬Q → ¬P, then you can take one of the given choices, using the following help:

law of detachment:

(P∧Q) ∧ P => Q

law of contraposition:

(P → Q) ≡ (¬Q → ¬P)

converse of P → Q:

Q → P

inverse of P → Q:

¬P → ¬Q

law of syllogism (transitivity):

(P → Q) ∧ (Q → R) => (P → R)

disjunctive syllogism:

[P → (Q ∨ R)] ∧ ¬R => (P → Q)

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