Lab2 #183, #202

[gmc0627]

#183:
For (1) x square is greater than 1, the instructor did not test for negatives, so he arrived at answer A. But if he tested negatives (ex. +2, -2) shouldn't the answer be C?

#202
(1) 1/K>0
The instructor did not test for a fraction (for example, if K=1/2 then 2>0), so he arrived at answer A. But if he tested for negatives, shouldn't the answer be E?

[StaceyKoprince]

#183. The question here is "is x^2 > x?" Any negative number will return the same answer to that question as any positive number that is greater than 1. Namely, yes, x^2 is greater than x. Remember that when you square a negative number, it becomes positive, and a positive number (x^2) is always greater than a negative number (x). In this case, you can test a negative (and you should, when you can - good instincts!), but it will not change your answer.

#202. You first say that the instructor didn't test for a fraction and then said "if he tested for negatives, shouldn't the answer be..." I assume you meant to say fractions again, not negatives? And did you want to test these for both statements?

In statement 1, 1/k > 0, you can try a positive fraction, yes (you can't try a negative fraction, though, because it will make the statement false). I can test a positiive fraction (and, again, you should when you can!), but it will not change your answer. k is still greater than zero. You are not permitted to test a negative fraction (you can only try numbers that make that statement true).

In statement 2, k^2 > 0, now you could try both positive and negative fractions. Once again, your answer (yes and no, which equals not sufficient) does not change.