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Topic
Use the \(\forall \) or \(\exists \) notation to write the following clauses:
a) There is an integer that is not divisible by itself;
b) There is a real number whose square plus 1 equals 0;
c) Every positive integer is greater than its reciprocal;
d) Every real number is greater than its counterpart.
Solution method – See details
Rewrite the clause as \(\forall x \in X,P(x)\) or \(\exists x \in X,P(x)\)
Detailed explanation
a) \(\exists x \in \mathbb{Z},x\cancel{ \vdots }x\)
b) \(\exists x \in \mathbb{R},{x^2} + 1 = 0\)
c) \(\forall x \in \mathbb{N}*,x > \frac{1}{x}\)
d) \(\forall x \in \mathbb{R},x > – x\)
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Source link net do edu