[ad_1]

**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) \(\forall x \in \mathbb{R},x > – x\)

[ad_2]

Source link net do edu