Download App

Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets5 Marks
Question
For three sets A, B and C, show that.
$\text{A}\cap\text{B}=\text{A}\cap\text{C}$ need not imply B = C.
✓

Answer

Let A = {1, 2, 3}, B = {2, 4, 6} and C = {2, 5, 7}
Then,
$\text{A}\cap\text{B}=\{2\}$
and $\text{A}\cap\text{C}=\{2\}$
Hence, $\text{A}\cap\text{B}=\text{A}\cap\text{C},$ but clearly $\text{B}\not=\text{C}.$

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 "5 Marks Questions" from Sets→Sets — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $A$ and $B$ are mutually exclusive events such that $P(A) = 0.35$ and $P(B) = 0.45$, find:
  1. $\text{P}(\text{A}\cup\text{B})$
  2. $\text{P}({\text{A}}\cap{\text{B}})$
  3. $\text{P}({\text{A}}\cap\overline{\text{B}})$
  4. $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
→
$\sin5\text{x}=5\cos^4\text{x}\sin\text{x}-10\cos^2\text{x}\sin^3\text{x}+\sin^5\text{x}$
→
Match each item given under the column $C_1$ to its correct answer given under the column $C_2.$
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
 
$C_1$
   $C_2$
$(a)$
Boys and girls alternate.
 $(i)$ $5! \times 6!$
$(b)$
No two girls sit together.
 $(ii)$ $10! – 5! 6!$
$(c)$
All the girls sit together.
 $(iii)$ $(5!)^2+ (5!)^2$
$(d)$
All the girls are never together.
 $(iv)$ $2!\  5!\  5!$
→
Prove that $\frac{1}{\text{n}+1}+\frac{1}{\text{n}+2}+...+\frac{1}{2\text{n}}>\frac{13}{24},$ For all natural numbers n > 1.
→
The income of a person is ₹ 300,000 in the first year and he receives an increase of ₹ 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.
→
Differentiate the following from the first principle$\text{x}\cos\text{x}$
→
If $\text{a}\cos2\theta+\text{b}\sin2\theta=\text{c}$ has $\alpha$ and $\beta$ as its roots, then prove that $\tan\alpha+\tan\beta=\frac{2\text{b}}{\text{a+b}}.$
[Hint: Use the identities $\cos2\theta=\frac{1-\tan^2\theta}{1+\tan^2\theta}$ and $\sin2\theta=\frac{2\tan\theta}{1+\tan^2\theta}\Big].$
→
In a town of $10,000$ families it was found that $40\%$ families buy newspaper $A, 20\%$ families buy newspaper $B, 10\%$ families buy newspaper $C, 5\%$ families buy $A$ and $B, 3\%$ buy $B$ and $C$ and $4\%$ buy $A$ and $C.$ If $2\%$ families buy all the three newspapers. Find
  1. The number of families which buy newspaper $A$ only.
  2. The number of families which buy none of $A, B$ and $C.$
→
The age distribution of 100 life-insuance policy holders is an follows:
Age (on nearest birth day)
17-19.5
20-25.5
26-35.5
36-40.5
41-50.5
51-55.5
56-60.5
61-70.5
No. of persons
5
16
12
26
14
12
6
5
→
If $\frac{2\sin\alpha}{1+\cos\alpha+\sin\alpha}=\text{y},$ then prove that $\frac{1-\cos\alpha+\sin\alpha}{1+\sin\alpha}$ is also equal to y.
$\Big[\text{Hint: Express }\frac{1-\cos\alpha+\sin\alpha}{1+\sin\alpha}=\frac{1-\cos\alpha+\sin\alpha}{1+\sin\alpha}.\frac{1+\cos\alpha+\sin\alpha}{1+\cos\alpha+\sin\alpha}\Big]$
→