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Math Help - More Logic

  1. #1
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    More Logic

    "A whole number x is odd only if x^2 is an odd whole number."

    a) Write it as a conditional statement.
    b) Write it's reciprocal.
    c) Write its counterpositive.

    " If A and B are sets, and A is a subset of B, then A U B = B."

    a) Write its reciprocal.
    b) Write its counterpositive.
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  2. #2
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    "P only if Q."

    a) Write it as a conditional statement. P \to Q
    b) Write it's reciprocal (converse?). Q \to P
    c) Write its counterpositive. (contrapositive?)  \neg Q \to \neg P<br />
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  3. #3
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    ok i think i figured it out for the first one, but in the second problem, which is p and which is q? im confused, thanks
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  4. #4
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    P="A and B are sets, and A is a subset of B" and Q="A U B = B."
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  5. #5
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    Please tell me if my answers are right.

    More Logic
    "A whole number x is odd only if x^2 is an odd whole number."

    a) Write it as a conditional statement. x is odd only if x^2 is odd.
    b) Write it's reciprocal. x^2 is odd if x is odd.
    c) Write its counterpositive. x^2 is not odd if x is not odd.

    " If A and B are sets, and A is a subset of B, then A U B = B."

    a) Write its reciprocal. A U B = B only if A and B are sets, and A is a subset of B.
    b) Write its counterpositive. A U B is not equal to B if A and B are not sets, and A is not a subset of B.
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  6. #6
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    Sorry. But none of those is correct.
    Here is the first one.
    If A whole number x is odd then x^2 is an odd whole number.
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    Wait, so i have to use if and then for every one? im at a loss
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  8. #8
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    Quote Originally Posted by NeedHelp18 View Post
    Wait, so i have to use if and then for every one? im at a loss
    Yes, that is the whole point.
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  9. #9
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    ohh ok i get it, so other than inserting if, and then, are they correct?
    especially the second problem
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  10. #10
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    Quote Originally Posted by NeedHelp18 View Post
    Wait, so i have to use if and then for every one? im at a loss
    What you have to keep in mind is that it's not the order of the way you write it that makes the logic, but the prepositions, namely if (and then)

    Think of it : P \Rightarrow Q is translated into "If P, then Q" or "Q, if P" or "P, only if Q"
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  11. #11
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    Quote Originally Posted by NeedHelp18 View Post
    ohh ok i get it, so other than inserting if, and then, are they correct?
    especially the second problem
    Yes, if you "move" the ifs/thens correctly.
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