# Thread: rules of inference for quantified statements

1. ## rules of inference for quantified statements

∼(∀x,P(x))

propositional function "x ≥ x^2

is true or false

Could someone tell me if I am correct, if not please explain:

∼(∀x,P(x)) = true

Basically I just prove that (∀x,P(x)) = true and then use the not operator to convert my answer to false.

Is this a correct way to prove this?

2. Basically I just prove that (∀x,P(x)) = true
Please show how you prove this.

and then use the not operator to convert my answer to false
So, if you apply negation to both sides of (∀x,P(x)) = true (assuming it is correct), why do you have ∼(∀x,P(x)) = true written above?

3. I made a mistake: (∀x,P(x)) = false

when x = 2, then x ≥ x^2 = false

so I then use the not operator to convert my answer to true which give me the final answer: ∼(∀x,P(x)) = true

4. could it be better explained this way:

∼(∀x,P(x)) = true

x^2 ≥ x is false when x = 2

∃x, ~P(x)

there exists at least one x that is not true

5. This seems fine.

6. OK thanks, I think i have this figured out.