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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