# Thread: Logical question clarification

1. ## Logical question clarification

I am again working on a homework assignment. I am just doing this for clarification purposes. I have an answer to a question, but I would like to double check if my answer is correct.

Question: Suppose that r is false, but that (p q) (r ∧ q) is true. Is p true or false? What about q?

Answer: I constructed a truth table to help me to solve this problem. After constructing and completing a truth table, I have come up with the answers that p is false and q is true.

I was just curious to know if this answer is correct.

2. ## Re: Logical question clarification

why not post your truth table so we can take a look.

my 30 second back of envelope calc doesn't agree with your answer.

3. ## Re: Logical question clarification

Hello, needhelp101!

$\displaystyle \text{Suppose }r\text{ is false and }\,(p\to q)\:\longleftrightarrow\:(r\wedge q)\,\text{ is true.}$
$\displaystyle \text{Is }p\text{ true or false? \;What about }q?$

I constructed a truth table to help me to solve this problem.
I have come up with: p is false and q is true.

Your values are reversed . . . an oversight?

If $\displaystyle r$ is false, then $\displaystyle (r\wedge q)$ is false.

Since the two parts are equivalent, $\displaystyle (p\to q)$ must also be false.

And $\displaystyle (p\to q)$ is false for $\displaystyle T\to F.$

$\displaystyle \text{Therefore, }p\text{ is true and }q\text{ is false.}$

4. ## Re: Logical question clarification

I apologize for not putting up my truth table. here is my truth table.

Actually, after taking a look at my truth table again, I had made a mistake and it was an oversight. I do apologize for that, and thank you all for your help. I feel dumb.

5. ## Re: Logical question clarification

you just misread your truth table when getting the answer.