What does this quantifier evaluates to?

Question

I need help solving the following question, Suppose U=Z. Simplify the quantifer, and say that if it is true or false with the help of and example,

~$\exists$x $(x| x|5 \Rightarrow x|15)$

Note that |= modulo.

Now for all values it evaluates to false for me but I am not getting sure of my answer. Also I would like to mention that I just used x=0,x=1 to find out if the statement is true and false. Can there be any case that it evaluates to true?

EDIT:

Thanks for the answers.
I tried solving it again and I have done it till, ~Ex(x|x|5->x|15)
Vx~(x|x|15->x|15)
As we know that ~(p->q)= ~pVq
therefore,
V(~(x|5))V(x|15)
Disproving by counter example,
I am out of ideas for the counter example, can anyone please give me a hint?

Thanks

@KaratugOzanBircan: Yes it does mean that but why should I take x=5? — , Nov 05 '11 at 11:59

score 4 · Answer 1 · answered Nov 05 '11 at 12:01

4

I think you mean $\exists$ by E.

So, "~$\exists x : x | 5 \Rightarrow x|15$" means "There is no x such that if x divides 5, then it divides 15." Take x=5 and this is a counterexample. Hence the statement is false.

answered Nov 05 '11 at 12:01

Karatuğ Ozan Bircan

4,299

2

you may use $\nexists$ notation – Pedja Nov 05 '11 at 12:13

What does this quantifier evaluates to?

EDIT:

1 Answers1