Question

Which algebraic property is not true for the set of real numbers R?

(a) For all a ≠ 0, b ∈ R such that a.b = 1 implies b = 1/ a.

(b) a. (1/ a) = 1 for all a ≠ 0.

(c) √a

2 = a for all a ∈ .

(d) If a.b > 0 then either a > 0 and b > 0 or a < 0 and b < 0.​

Answer 1

Concept:-

It is set related question. There are many properties for a set of real numbers.

Given:-

(a) For all a ≠ $0$, b ∈ R such that a.b = $1$ implies b = $1$/ a.

(b) a. ($1$/ a) = $1$ for all a ≠ $0$.

(c) √$a^{2}$ = a for all a ∈ .

(d) If a.b > $0$ then either a > $0$ and b > $0$ or a < $0$ and b < $0$

Find:-

Which property is not true from the above options.

Solution:-

The correct option is c) $\sqrt{a^{2}} =$a for all a ∈, because it is only possible when the value of a is a whole number.