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Math Help - convers and contrapositive question

  1. #1
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    galway
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    convers and contrapositive question

    Could some one with more knowledge than me just confirm if i am doing the right thing here, Thanks.

    State
    (i) the converse, and
    (ii) the contrapositive
    of the following implication:

    if a > b and b > c and a > c

    (i) a > c only if a > b and b > c
    (ii) if c > a then b > a and c > b
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  2. #2
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    Re: convers and contrapositive question

    The terms "converse" and "contrapositive" apply only to statements of the form "If A Then B". In that case the "converse" is "If B Then A" and the "contrapositive" is "If NOT B then NOT A".

    But you do NOT have an implication here because you have no "then".

    You probably mean "if a> b an b> c then a> c". (Which is true.)

    The "converse" is "if b> c then a>b a and b>c" (Which is not true.) The "only if" formulation is equivalent to the "if then" formulation but "if X then Y" is equivalent to "X only if Y". You have "X" and "Y" reversed.

    The contrapositive is "if NOT (a> c) then NOT (a> b and b> c)". We can reduced that a little by using the fact that "NOT (X and Y)" is the same as "NOT X or NOT Y" as well as the fact that "NOT x> y" is the same as " x\le y" to write the contrapositive as "if a\le c then either a\le b or b\le c". (which is true. The contrapositive of a statement is true if and only if the statement is true.)

    You seem to think that "NOT x> y" is the same as "x< y" (y> x) but that is not true. If x= y then "NOT x> y".
    Thanks from ronanbrowne88
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  3. #3
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    Re: convers and contrapositive question

    Quote Originally Posted by HallsofIvy View Post
    The "converse" is "if b> c then a>b a and b>c" (Which is not true.) The "only if" formulation is equivalent to the "if then" formulation but "if X then Y" is equivalent to "X only if Y". You have "X" and "Y" reversed.
    Thanks for the help the makes things clearer, i presume that extra a above is a typo , after a >b?
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