\( \left\lvert\, \begin{array}{l}\text { Exercice 3: } \\ \text { Déterminer la valeur de vérité de chacune des } \\ \text { propositions suivantes : } \\ P_{1}: " 3 \times 0=0 \text { et } 3^{0}=1^{\prime \prime} ; P_{2}:\left(-\sqrt{2} \in \mathbb{Z} \text { ou } \sqrt{2} \prec 1^{\prime \prime}\right. \\ P_{3}: "(\exists n \in \mathbb{N}) ; \sqrt{3 n^{2}+1} \in \mathbb{N}^{\prime \prime} ; P_{4}: "(\forall x \in \mathbb{R}) ; x^{2} \succ 1^{\prime \prime} \\ P_{5}: "(x \in \mathbb{R}), x \succ 2 \Rightarrow x^{2} \succ 4^{\prime \prime} \\ P_{6}: "(x \in \mathbb{R})\left(x^{2}=1 \Rightarrow x=-1\right) \\ P_{7}: "(x \in \mathbb{R})(|x| \prec 1 \Leftrightarrow x \in]-1 ;[)\end{array}\right. \)
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