# Disprove the nested quantifier

#### albert1992

1. Homework Statement
∃x∀y(y̸=0→xy=1) in the real numbers universe.

2. Homework Equations

3. The Attempt at a Solution
Since the given statement is false I negated the whole statement to become

∀x∃y(y̸!=0^xy!=1) (!= means not equal to)

then I would have to prove this correct by setting y to something except zero
I cant find any y to prove this correct

Related Calculus and Beyond Homework Help News on Phys.org

#### Hurkyl

Staff Emeritus
Gold Member
I can't make sense of your formulae. I think you messed up the typesetting. Also, it may help to use words instead of symbols... especially if you have to improvise to make the symbols.

#### albert1992

there exists an x,for every y (if y does not equal to zero then x*y=1)

*real numbers universe

#### Mark44

Mentor
there exists an x,for every y (if y does not equal to zero then x*y=1)

*real numbers universe

For every nonzero y in R, there exists an x in R such that xy = 1.

#### albert1992

i have to disprove the statement since it is false

#### Dick

Homework Helper
there exists an x,for every y (if y does not equal to zero then x*y=1)

*real numbers universe
If y does not equal 0, then there is only one value x such that x*y=1. That's x=1/y. How can there be an x that has an infinite number of solutions to x*y=1?

#### albert1992

Exactly why the statement is false, but i have to prove that it is false
by negating the whole expression