Is inverse, converse, and contrapositive of a algebra statement true?

Posted on 2012-09-21
Last Modified: 2012-09-21
Consider following statement:

If x = y, then 5x = 5y                                 TRUE
Inverse:  If x != y, then 5x != 5y                TRUE
Converse:  If 5x = 5y, then x = y               TRUE
Contrapositive:  If 5x != 5y, then x != y     TRUE

This is high school geometry question.

I'm not a student.  I'm refreshing my geometry skills so I can help a student.
Question by:naseeam
    LVL 31

    Expert Comment

    For any well defined algebraic statements

    Statement1 = Statement2     then  X*Statement1 =X* Statement2

    Statement1 != Statement2     then  X*Statement1 !=X* Statement2    provided X! = 0

     X*Statement1 = X* Statement2    then Statement1 = Statement2    provided X! = 0

     X*Statement1 != X* Statement2    then Statement1 = Statement2

    Author Comment

    >  X*Statement1 !=X* Statement2  then Statement1 = Statement2

    Did you mean to say  Statement1 != Statement2
    LVL 31

    Accepted Solution

    I did sorry, was trying to edit it, ie

     X*Statement1 != X* Statement2    then Statement1 != Statement2

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