- #1
Rob Hal
- 13
- 0
Hi all,
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
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