## Solving Lesson 15 Page 9 Math Workbook 10 – Kite>

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