Can anyone please explain why the one is not the correct answer?

Let P(n,m) be a property about two integers n and m. If we want to disprove the claim that "For every integer n, there exists an integer m such that P(n,m) is true", then we need to prove that

1)There exists an integer n such that P(n,m) is false for all integers m.

2)For every integer m, there exists an integer n such that P(n,m) is false.

3)There exists integers n,m such that P(n,m) is false.

4)There exists an integer m such that P(n,m) is false for all integers n.

5)For every integer n, and every integer m, the property P(n,m) is false.

6)For every integer n, there exists an integer m such that P(n,m) is false.

7)If P(n,m) is true, then n and m are not integers.

1 answer

Why the 3rd one is not the correct answer and what is the correct answer?
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