1. ## Making a conjecture

-Determine whether the conjection is true or false. Give a counterexample for any false conjecture-

Given: m + y > 10, y > 4

Conjecture: m < 6

If I knew what in the world the ">" and "<" signs meant, I might be able to work the problem. Please could you tell me what > and < means? And how do you find whether it is true or false after that?

2. Originally Posted by Melancholy
-Determine whether the conjection is true or false. Give a counterexample for any false conjecture-

Given: m + y > 10, y > 4

Conjecture: m < 6

If I knew what in the world the ">" and "<" signs meant, I might be able to work the problem. Please could you tell me what > and < means? And how do you find whether it is true or false after that?
> -- Greater Then or Equal To

< -- Less Than or Equal To

Let's see what you get.

3. Okay, so that one I already knew sorta... the line under it was confusing me... but I don't understand what I'm supposed to do still...

If m + y > 10 and y > 4

What does m < 6 have to do with it? Uhg... need more explanation...

4. Originally Posted by Melancholy
Okay, so that one I already knew sorta... the line under it was confusing me... but I don't understand what I'm supposed to do still...

If m + y > 10 and y > 4

What does m < 6 have to do with it? Uhg... need more explanation...
look at it this way:

let's say $\displaystyle x \ge 4$

then what is likely to be true for $\displaystyle x + 1$?

well, since $\displaystyle x \ge 4$, if we add 1, then $\displaystyle x + 1 \ge 5$, since we added one more to both sides.

is it possible that $\displaystyle x + 1 \leq 5$? yes, only if $\displaystyle x = 4$, but otherwise, no. in general, it will be the case that $\displaystyle x + 1 \ge 5$, since $\displaystyle x$ can be 4 or greater, adding 1 makes it 5 or greater