Download App

Relation — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRelation2 Marks
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: $(\text{a},\text{b})\text{ R }(\text{a, b})\text{ for all }(\text{a, b})\in\text{N}\times\text{N}$
✓

Answer

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

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

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\frac{2^{-\cos\text{x}}-1}{\pi\big(\text{x}-\frac{\pi}{2}\big)}$
→
Find the general solutions of the following equations: $\sec\text{x}=\sqrt{2}$
→
One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
→
Find the sum of the following arithmetic progression: $(x - y)^2, (x^2 + y^2), (x + y)^2$ ... to $n$ terms.
→
If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and $\text{P}(\text{A}\cup\text{B})=0.5,$ find $\text{P}(\text{A}\cap\text{B}).$
→
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?
$(\text{a, b}):\text{R }\text{for all a}\in\text{N}$ 
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\sin2\text{x}}{\text{e}^\text{x}-1}$
→
A line a drawn through A (4, -1) parallel to the line 3x - 4y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.
→
Prove that: $(\sin^3\text{x}+\sin\text{x})\sin\text{x}+(\cos3\text{x}-\cos\text{x})\cos\text{x}=0$
→