Question

Select the choice (or choices) below which could be not used in a counterexample to show that a-|b-c|=a+|-b+c| is false.

a. a=b=c=1
b. a=2, b=3, c=4
c. a=b=-1, c=-2
d. a=0, b=1, c=-2
e. a=3, b=c=-2

Answer 1

A counter example aims to show something which claims to be true for a set of elements to be false for at least one of those elements.

Here, a counter example would be the selection of a set of points that WOULD show the statement as false. Though, you're being asked to find those sets of numbers that WOULDN'T show this statement to be false.

Testing the points in (a) will show the left-hand side equals the right-hand side...so these points COULDN'T be used as a counter example, which is what you're being asked to find. So (a) is one of your choices.

(b), on the other hand, would yield left-hand side = 1 and right-hand side = 3. Since the LHS and RHS aren't equal, the statement (equation) fails here. These points COULD be used for a counter example, so leave them.

Keep going with this.

Hope it helps.