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!

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

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

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

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

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

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.