# math

posted by .

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 -

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)

## Similar Questions

1. ### English

Can you please tell me if all the alternatives I included are correct?
2. ### math

please help... determine if the argument is valid or invalid along with the appropriate form of argument. if harvard hustles then harvard wins harvard wins ___________________ harvard hustles are these statements: valid by law of detachment …
3. ### Math-geometry

Determine if the argument is valid or invalid. Give a reason to justify answer. If the bell rings, then we answer the door. The bell rings. We answer the door.
4. ### philosophy

Truth tables can determine which of the following?
5. ### PHI 103

"All dogs hate cats. Sirius is a dog. So Sirius hates cats" is an example of a (Points : 1) sound inductive argument. valid deductive argument. invalid inductive argument. weak deductive argument. I am confused a little about this …
6. ### English

1. Because she felt cold, Susan put on her coat. 2. Because Susan felt cold, she put on her coat. 3. Feeling cold, Susan put on her coat. (Which one is correct?
7. ### Math for Liberal Arts

Directions: Define the necessary symbols, rewrite the argument in symbolic form, and us a truth table to determine whether the argument is valid. If the argument is invalid, interpret the specific circumstances that cause the argument …
8. ### math for liberal arts

construct a truth table to determine whether each argument is valid. Be sure to state whether it is valid or invalid with each question. 1) ~p v q p ____ triangle of dots p^~q
9. ### guidance

Four-year-old Nathan refuses to put on his coat before going out to play on a chilly day. Using guidance techniques, you should say, A. "No coat, no play, period."B. "Put that coat on this instant."C. "You're putting that coat on, …
10. ### guidance

Four-year-old Nathan refuses to put on his coat before going out to play on a chilly day. Using guidance techniques, you should say, A. "No coat, no play, period."B. "Put that coat on this instant."C. "You're putting that coat on, …

More Similar Questions