Let R be a relation from N to N defined by R= (a, b):a, b and a=b… - Vidyadip

Question

Let R be a relation from N to N defined by $\text{R}=\{(\text{a, b}):\text{a, b}\in\text{N and a}=\text{b}^2\}.$ Are the following statement true?
$(\text{a, b})\in\text{R and (b, c)}\in\text{R}\Rightarrow \text{(a, c)}\in\text{R}$

✓

Answer

We have,
$\text{R}=\{(\text{a, b}):\text{a, b}\in\text{N and a}=\text{b}^2\}$
This statement is not true because $(36,6)\notin\text{R and (25, 5)}\in\text{R}\text{ but }(36,5)\notin\text{R}$

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 "3 Marks Question" from Relations→Relations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $a, b, c$ and d are in G.P show that $(a^2+ b^2+ c^2) (b^2+ c^2+ d^2) = (ab + bc + cd)^2.$

Write the complex number $ z = \frac { i - 1 } { \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } }$ in the polar form.

Find the coordinates of the foot of perpendicular from the point (-1, 3) to the line 3x - 4y - 16 = 0

If $\text{x}=\frac{\text{b}}{\text{a}},$ find the value of $\sqrt{\frac{\text{a+b}}{\text{a - b}}}+\sqrt{\frac{\text{a - b}}{\text{a+b}}}.$

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and three edges passing through the origin coincides with the positive direction of the axes through the origin?

Find the middle terms(s) in the expansion of:
$\Big(\frac{\text{p}}{\text{x}}+\frac{\text{x}}{\text{p}}\Big)^{9}$

A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

Find the mean deviation about the median for the data in: $36, 72, 46, 60, 45, 53, 46, 51, 49,42$

Find the value of ${({a^2} + \sqrt {{a^2} - 1} )^4} + {({a^2} - \sqrt {{a^2} - 1} )^4}$

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.