I have to see if the following statements are true.
A) $\forall x \in \mathbb Z, x^2 \le 1000 $
If it not true than find an counterexample
B) $\exists x \in \mathbb R,$ such that $x^2 \lt 1 $
If it is true, than find an example.
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For A) I think its not true because what if x = 1001. But what would be the counter example?
For B) I think its true because it has to be true for atleast once. So if I put x = -1, its true.
If I'm wrong please let me know.
Yes, A) is false. You've just given us a counterexample ($x = 1001$).
Yes, B) is true, but your example does not work ($(-1)^2 = 1 \geq 1$).