Download App

MATHEMATICAL REASONING — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSMATHEMATICAL REASONING3 Marks
Question
Show that the statement “For any real numbers a and b, $\text{a}^2=\text{b}^2$ implies that $\text{a = b}$” is not true by giving a counter-example.
✓

Answer

The given statement can be written in the form of “if-then” as follows.If a and b are real numbers such that $\text{a}^2=\text{b}^2,$ then $\text{a = b}.$
Let p: a and b are real numbers such that $\text{a}^2=\text{b}^2.$
$\text{q}:\text{a = b}$
The given statement has to be proved false. For this purpose, it has to be proved that if $\text{p},$ then $\sim\text{q}.$ To show this, two real numbers, a and b, with $\text{a}^2=\text{b}^2$ are required such that $\text{a}\neq \text{b}.$
Let $\text{a}=1$ and $\text{b}=-1$
$\text{a}^2=(1)^2=1$ and $\text{b}^2=(-1)^2=1$
$\therefore\text{a}^2=\text{b}^2$
However, $\text{a}\neq \text{b}$
Thus, it can be concluded that the given statement is false.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 3 marks)" from MATHEMATICAL REASONING→MATHEMATICAL REASONING — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4, 3) and (– 1,4).
→
In an examination, a question paper consists of 12 questions divided into two parts i.e. Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
→
Find the domain of the following real valued functions of real variable: $\text{f(x)}={\sqrt{\frac{\text{x}-2}{3-\text{x}}}}$
→
Find the distances of the point P(-4, 3, 5) from the coordinate axes.
→
Find the real values of $\theta$ for which the complex number $\frac{1+\text{i}\cos\theta}{1-2\text{i}\cos\theta}$ is purely real.
→
Find the sum to n terms of the series $1 \times 2 \times 3 + 2 \times 3 \times 4 + 3 \times 4 \times 5 + \ldots$
→
Prove that: $\sin^242^\circ-\cos^278^\circ=\frac{\sqrt{15}+1}{8}$
→
Prove that: $^{4\text{n}}\text{C}_{2\text{n}}:^{2\text{n}}\text{C}_{\text{n}}=[1,3,5...(4\text{n}-1):[1,3,5...(2\text{n-1})^{2}].$
→
Differentiate the following from first principle: $\text{k}\text{x}^\text{n}$
→
If $\frac{1}{\text{a}+\text{b}},\frac{1}{2\text{b}},\frac{1}{\text{b}+\text{c}}$ are three consecutive terms ofan A.P., prove that a, b, c are the three consecutive terms of a G.P.
→