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**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?