Set Theory Logic Question

1. The problem statement, all variables and given/known data
In each of the two following open sentences P(x) and Q(x) over a domain S are given.
Determine all ##x \in S## for which P(x) → Q(x) is a true statement.

## P(x): x \in [-1, 2]; Q(x): x^{2} \leq 2; S=[-1,1] ##

2. Relevant equations
According to truth values for →:
a b a-> b
0 0 1
0 1 1
1 0 0
1 1 1
3. The attempt at a solution
If I can prove that P is False, then I will always get a T value for ->
Can I just say ## x \in [-1,1] ##, this would literally mean that statement P is false.
Could this count?
 
Would this mean that the statement is true vacuously?
 

vela

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Is there any ##x \in S## such that P(x) is false?
 

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