Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

If I have these two statements given to me, and I have to determine whether they are true or not.

a) [tex] \forall x \epsilon R [/tex] [tex]\exists y \epsilon R [/tex] [tex](y^2 = x^2 + 1)[/tex]

b) [tex]\exists y \epsilon R [/tex] [tex]\forall x \epsilon R [/tex] [tex](y^2 = x^2 + 1) [/tex]

Now, to me, they both mean exactly the same thing, and both can be shown to be false by setting x = 2, then y is not a real number.

However, seeing that the question specifically asks to prove just those two statements, I'm wondering if perhaps I am interpreting them wrong and they actually mean two different things.

Thanks in advance for any advice,

Robbie

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mathematical Proofs

**Physics Forums | Science Articles, Homework Help, Discussion**