Download App

Sets — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSets4 Marks
Question
Find sets A, B and C such that $\text{A}\cap\text{B},\text{ A}\cap\text{C and B}\cap\text{C}$ are non-empty sets and $\text{A}\cap\text{B}\cap\text{C}=\phi.$
✓

Answer

To find sets A, B and C such that $\text{A}\cap\text{B}\not=\phi,\ \text{A}\cap\text{C}=\phi$ and $\text{B}\cap\text{C}=\phi,\text{ and }\text{A}\cap\text{B}\cap\text{C}=\phi$ Take $\text{A} = \{1, 2, 3\}$ $\text{B} = \{2, 4, 6\}$ and $\text{C} = \{3, 4, 7\}$ Then, $\text{A}\cap\text{B}=\{2\}$ $\therefore\text{A}\cap\text{B}\not=\phi$ $\text{A}\cap\text{C}=\{3\}$ $\therefore\text{A}\cap\text{C}\not=\phi$ $\text{B}\cap\text{C}=\{4\}$ $\therefore\text{B}\cap\text{C}\not=\phi$ However A, B and C have no elements in common, $\therefore\text{A}\cap\text{B}\not=\phi.$

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

If a and b are the roots of $\text{x}^2-3\text{x}+\text{p}=0$ and c, d are roots $\text{x}^2-12\text{x}+\text{q}=0,$ where a, b, c, d from a G.P. Prove that (q + p) : (q - p) = 17 : 15.
→
Find the equation of an ellipse whose eccentricity is $\frac{2}{3},$ the latus-rectum is $5$ and the centre is at the origin.
→
Prove that: $\frac{\sin11\text{A}\sin\text{A}+\sin7\text{A}\sin3\text{A}}{\cos11\text{A}\sin\text{A}+\cos7\text{A}\sin3\text{A}}=\tan8\text{A}$
→
Differentiate the following from first principle:$\sqrt{2\text{x}^2-1}$
→
Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of -6 - 24i.
→
Differentiate the following from the first principle$\sin\text{x}+\cos\text{x}$
→
If the function f(x) satisfies $\lim\limits_{\text{x}\rightarrow1}\frac{\text{f}(\text{x})-2}{\text{x}^2-1}=\pi$ , evaluate $\lim\limits_{\text{x}\rightarrow1}{\text{f}(\text{x})}$.
→
Prove that: $\frac{\sin(\theta+\phi)-2\sin\theta+\sin(\theta-\phi)}{\cos(\theta+\phi)-2\cos\theta+\cos(\theta-\phi)}=\tan\theta$
→
Given that $\bar x $ is the mean and ${\sigma ^2}$ is the variance of n observations $x_1, x_2, ..... x_n$ Prove that the mean and variance of the observation $ax_1, ax_2, .... ax_n$ are $a$$\bar x$ and $a^2{\sigma ^2}$ respectively $(a \ne 0)$
→
Find the equations of the straight lines passing through $(2, -1)$ and making an angle of $45°$ with the line $6x + 5y - 8 = 0$.
→