let me use Ax as "for all" and Ex as "for some" or "there exsists.
now my question is, what is the truth value of:
Ax[(x^2=1) implies (x=-1)] u=R
What you wrote reads:
For all x^2 = 1 implies x = -1.
Does the u=R at the end mean that R (the reals) is the universal set? If so, I think you meant:
For all x in R, x^2 = 1 implies x = -1.
Now to make this statement false, all we have to do is find 1 value x in the reals, such that x^2 = 1 and x <> -1. (<> means does not equal).
Can you find it?
There might be a mistake. Why didn't you use Ex?
IPBLE: Increasing Performance By Lowering Expectations.
I don't think so krassi. It's a good example of how to negate the all quantifier, as well as a good example that shows what breaks down when a function isn't 1-1, if I interpreted it right. Seems to unlikely to just be chance...