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)

## Answer this Question

## Related Questions

- English - 1. Because she felt cold, Susan put on her coat. 2. Because Susan felt...
- guidance - Four-year-old Nathan refuses to put on his coat before going out to ...
- guidance - Four-year-old Nathan refuses to put on his coat before going out to ...
- Math-geometry - Determine if the argument is valid or invalid. Give a reason to ...
- English - Can you please tell me if all the alternatives I included are correct...
- math - please help... determine if the argument is valid or invalid along with ...
- math - if the temperatureis 39 degrees celsius you are most likely to want to ...
- Science - In a praticular breed of cattle, a black coat is dominant over a red ...
- Science - In a praticular breed of cattle, a black coat is dominant over a red ...
- Science - In a praticular breed of cattle, a black coat is dominant over a red ...