Download App

Sets — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSets3 Marks
Question
For any two sets, prove that:
$\text{A}\cap(\text{A}\cup\text{B})=\text{A}.$
✓

Answer

$\text{A}\cap(\text{A}\cup\text{B})=(\text{A}\cap\text{A})\cup(\text{A}\cap\text{B})$ $[\because\cap$ is distributive over $\cup]$
$=\text{A}\cup(\text{A}\cap\text{B})$ $[\because\text{A}\cap\text{A}=\text{A}]$
$=\text{A [using (i)]}.$

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 Sets→Sets — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

How many terms of the A.P. $-6,\ -\frac{11}{2},\ 5,\ ...$ are needed to give the sum -25?
→
Find equation of the line which is equidistant from parallel lines 9x + 6y - 7 = 0 and 3x + 2y + 6 = 0
→
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
→
Find the general solution of the equation $\sin\text{x}-3\sin2\text{x}+\sin3\text{x}=\cos\text{x}-3\cos2\text{x}+\cos3\text{x}$
→
Differentiate the following from first principle:

$\frac{1}{\sqrt{\text{x}}}$

→
The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
→
Which term of the sequence $12+8\text{i},\ 6\text{i},\ 10+4\text{i},\ ...$ is (a) real (b) purely imaginary?
→
Prove that: $^{4\text{n}}\text{C}_{2\text{n}}:^{2\text{n}}\text{C}_{\text{n}}=[1,3,5...(4\text{n}-1):[1,3,5...(2\text{n-1})^{2}].$
→
We wish to select 6 persons from 8 but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
→
Show that the points (5, 5), (6, 4), (-2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.
→