Let R be a relation on N × N defined by: (a, b) R (c, d) +d=b+c f… - Vidyadip

Question

Let R be a relation on N × N defined by: $(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$ Show that: $(\text{a},\text{b})\text{ R }(\text{c, d})\Rightarrow(\text{c},\text{d})\text{ R (a, b)}$ for all $\text{(a, b)(c, d)}\in\text{N}\times\text{N}$

✓

Answer

We have, $(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$ Now, (a, b) R (c, d) ⇒ a + d = b + c ⇒ c + b = d + a ⇒ (c, d) R (a, b)

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 2 marks)" from Relation→Relation — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A point R with x-coordinate 4 lies on the line segment joining the points P(2, -3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint Suppose R divides PQ in the ratio k : 1. The coordinates of the point R are given by $\left(\frac{8 k+2}{k+1}, \frac{-3}{k+1}, \frac{10 k+4}{k+1}\right)$].

One die of red colour, one of white colour and one of blue colour are placed, in a bag. One die is selected at random and rolled, its colour and the number on its upper most face is noted. Describe the sample space.

Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x).

Prove that: $\cos55^\circ+\cos65^\circ\cos175^\circ=0$

Differentiate the following function with respect to $\text{x}$:$\text{x}^2\text{e}^\text{x}\log\text{x}$

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

In a $\triangle\text{ABC},$ if $\text{a}=\sqrt{2},\text{b}=\sqrt{3}$ and $\text{c}=\sqrt{5},$ show that its area is $\frac{1}{2}\sqrt{6 }\text{ sq. units.}$

A line passes through $(x_1, y_1)$ and $(h, k)$. If slope of the line is m, show that $k - {y_1} = m(h - {x_1})$.

Evaluate $\mathop {\lim }\limits_{x \to - 1} \frac{{{x^{10}} + {x^5} + 1}}{{x - 1}}$

Determine the domain and range of the following relations: $\text{S}=\{(\text{a, b}):\text{b}=|\text{a}-1|,\text{ a}\in\text{Z and |a|}\leq3\}$