Question

Conjecture: |x| = c iff x = c or x = -c

steps:

1) x≥0 or x<0

2) x≥0 or x<0

3) so c = x, by hypothesis

4) If x < 0 then by definition |x| = x

5) By hypothesis |x| = c

6) so -x = c

7) and x = -c

My questions are:

a. Prove that the conjecture is false

b. check if each step in the argument is false

c. why is this not a proof?

d. Fix the conjecture by stating a similar result that begins “|x| = c iff…” and then prove it

Thank you!