Question

I need help with this problem. Am i missing another column for my table?

Answer 1

For 2c

Answer 2

My work:

Answer 3

@Hero

Answer 4

\(0\in \mathbb{R}\)

Answer 5

To prove it you have to show it is true for all of the following cases:
x < 0 and y < 0
x < 0 and y >= 0
x >=0 and y < 0
x >= 0 and y > =0
x = y
x > y
x < y

Answer 6

hmm whys that?

Answer 7

I see we are trying to prove it is false. So just find one counterexample

Answer 8

But if it were true then you would have to show for all those cases.

Answer 9

i see, But for the column Y, do we pick 1 or can it be any other number?

Answer 10

There's no need to do all the symbolism unless you're trying to prove it is true or unless your instructor requires it. If it is false, just find the counterexample.

Answer 11

Y doesn't have to be 1

Answer 12

oh, how come from last nights example, the column y was all 1's

Answer 13

im confused lol

Answer 14

i did an edit for it.

Answer 15

You just have to find the counterexample. That's it. Don't worry about the other problem. It was just used to do it the way the book wanted which was to create a table testing values. If the question just asked to find the counterexample like this one, then I would have just found the counterexample and have been done with it. You don't need to provide a table for this one.

Answer 16

oh okay, he usually wants us to do a table for it. Dont we usually negate the original stmt so we can can find a false stmt.

Answer 17

this problem is weird since we didnt have a hypothesis since we usually want the hypothesis to be true and conclusion to be false.

Answer 18

That's because you have to set the condition. You don't have to do a table for this one. The table requirement was tor the other problems. Have you found the counter example yet?

Answer 19

for this one yes, which was x= 0 and y = 2

Answer 20

It also works if either x or y is negative

Answer 21

i messed up on the last line. It suppose to be " If x = 0 and y = 2, then we obtain 2 ≥0, which is false. "

Answer 22

oh thats right, since it says real numbers.

Answer 23

Anyway, it's not necessary to do more than what is required for these. If it says find a counterexample, then find a counterexample and move on to the next one.

Answer 24

okie :)