Solving Lesson 15 Page 9 Math Workbook 10 – Kite>

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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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