Download App

Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets4 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 "(Each question 4 marks)" from Sets→Sets — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the center, eccentricity, foci and directrices of the hyperbola $\text{x}^{2}-3\text{y}^{2}-2\text{x}=8.$
→
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\sin\sqrt{\text{x}}-\sin\sqrt{\text{a}}}{\text{x}-\text{a}}$
→
Evaluate the following limit: Evaluate: $\lim\limits_{\text{n}\rightarrow\infty}\frac{1^4+2^4+3^4+\ \cdots+\text{n}^4}{\text{n}^5}-\lim\limits_{\text{n}\rightarrow\infty}\frac{1^3+2^3+\ \cdots+\text{n}^3}{\text{n}^5}$
→
In each the following find the equation of the hyperbola satisfying the given conditions: Foci $(0, \pm13), $ conjugate axis = 24
→
If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.
→
If $\text{A}\times\text{b}\subseteq\text{C}\times\text{D and A}\times\text{B}=\phi,$ prove that $\text{A}\subseteq\text{C and B}\subseteq\text{D}$
→
Differentiate the following functions with respect to x:$\frac{\sin\text{x}-\text{x}\cos\text{x}}{\text{x}\sin\text{x}+\cos\text{x}}$
→
Calculate the mean, median and standard deviation of the following distribution:
Class-interval: 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70
Frequency: 2 3 8 12 16 5 2 3
→
If X lies in the first quadrant and $\cos\text{x}=\frac{8}{17},$ then prove that $\cos\Big(\frac{\pi}{6}+\text{x}\Big) +\cos\Big(\frac{\pi}{4}-\text{x}\Big)+\cos\Big(\frac{2\pi}{3}-\text{x}\Big)=\Big(\frac{\sqrt{3}-1}{2}+\frac{1}{\sqrt{2}}\Big)\frac{23}{17}$
→