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Hello,Scott!

Can you clear up this one that confuses me?

"Give a counterexample to show that the following statement is not always true for real numbers a, b, and c:

If a>b, then ac>bc"

A.a=3,b=4,c=2 3(2) is not greater than or equal to 4(2)

B.a=-3,b=4,c=2 -3(2) is greater than or equal to 4(2)

C.a=3,b=-4,c=2 3(2) is greater than or equal to -4(2)

D.a=3,b=4,c=-2 3(-2) is not greater than or equal to 4(-2)

The correct solution is given as a=3, b=4, c=-2, 3(-2)is not greater than or equal to 4(-2)

I don't get it! What the h___ is a counterxample?

Why is choice D. the correct answer?

This sounds like the kind of stuff that lawyers love.

Thanks

Chris

Upon getting this question, I too am confused. Send this question to the publisher of the book, for the correct answer is not found. It is known that with the thousands of problems in a book, an error is almost bound to occur somewhere.

A true counterexample would be to find a, b such that a>b with a value for c that makes ac<=bc.

For (A), a=3 is not greater than b=4, so it can't be used to show anything.

For (B), a=-3 is not greater than b=4, so it can't be used to show anything.

For (C), a=3 is greater than b=-4, but 3*2 = 6 is also greater than -4*2 = -8,

so this doesn't show anything is wrong.

For (D), a=3 is not greater than b=4, so it can't be used to show anything.

Perhaps the negative sign needs to be moved on (D).

I would use the number a=4, b=3, and c=-2.

That would say, using (D), since 4 > 3, deducing ac > bc does not work.

When, from what's given for values of a, b, and c, ac = -12 and bc = -6,

It can then be seen that ac is not greater than bc.

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Comment | This guy knows his stuff! Congrats! Chris |

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