Deductive Reasoning: the weather and the soccer game

Select the statement that is the negation of the statement, "If the weather is cold, then the soccer game will be played."

a. If the weather is not cold, then the soccer game will be played.
b. The weather is cold and the soccer game was not played.
c. If the soccer game is played, then the weather is not cold.
d. The weather is cold and the soccer game will be played.

p=the weather is cold
q=the soccer game will be played

p--->q the negation of that is not p and not q

meaning choice A is the correct answer?

Help with deductive reasoning problem.

Select the statement that is the negation of the statement, "If the weather is cold, then the soccer game will be played."

a. If the weather is not cold, then the soccer game will be played.
b. The weather is cold and the soccer game was not played.
c. If the soccer game is played, then the weather is not cold.
d. The weather is cold and the soccer game will be played.

p=the weather is cold
q=the soccer game will be played

p--->q the negation of that is not p and not q

meaning choice A is the correct answer?

Re: Deductive Reasoning

\(\displaystyle \neg \left( {A \to B} \right) \equiv A \wedge \neg B\)

Re: Deductive Reasoning

Do you know of what types of math books that can help me with those types of problems?
Any names of books that you suggest?

Re: Help with deductive reasoning problem.

How can we possibly do YOUR reasoning?

Re: Help with deductive reasoning problem.

Wouldn't a. need to read "If the weather is not cold, then the soccer game will NOT be played"?

My reasoning is that: "If the weather is cold, then the soccer game will be played." is basically (Weather = Cold AND Soccer=Played)

a. If the weather is not cold, then the soccer game will be played. (Weather <> Cold AND Soccer = Played)
b. The weather is cold and the soccer game was not played. (Weather = Cold AND Soccer <> Played)
c. If the soccer game is played, then the weather is not cold. (Weather <> Cold AND Soccer = Played)
d. The weather is cold and the soccer game will be played. (Weather = Cold AND Soccer = Played)