Question

Let p be "The two numbers are negative" and q be "Their product is positive" Which of the following statements best represents the statement p⟺q?Select the correct answer below:None of the aboveIf their product is positive, then the two numbers are negative.Their product is positive and the two numbers are negative.The two numbers are negative only if their product is positive.

Answer 1

We have the following facts:

p = The two numbers are negative

q = Their product is positive

We have the following statement:

`p\Leftrightarrow q`

We see that in the statement appears the symbol ⟺, this symbol must be interpreted as "if and only if".

Now, let's see the meaning of the options. Taking into account that the symbol ⇒ means "then".

1) If their product is positive, then the two numbers are negative. Is equivalent to:

`p\Rightarrow q`

So this is not the answer because we don't have a ⟺.

2) Their product is positive and the two numbers are negative.

`p\wedge q`

We see that in the sentence we an "and", we express that with the symbol ∧.

3) The two numbers are negative only if their product is positive.

This option is not correct because we don't have an "if and only if", we only have "only if".

Answer

Because none of options 1, 2 or 3 are equivalent to the statement of the question, we conclude that the correct option is: None of the above.