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Math Help - Logical question clarification

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    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.}
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  4. #4
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    Re: Logical question clarification

    I apologize for not putting up my truth table. here is my truth table. Logical question clarification-tt.jpg


    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.
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  5. #5
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    Re: Logical question clarification

    you just misread your truth table when getting the answer.
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