Download App

Relations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRelations4 Marks
Question
If $\text{A}\times\text{b}\subseteq\text{C}\times\text{D and A}\times\text{B}=\phi,$ prove that $\text{A}\subseteq\text{C and B}\subseteq\text{D}$
✓

Answer

Let (a, b) be an arbitrary element of A × B. then,
$(\text{a},\text{b})\in\text{A}\times\text{B}$
$\Rightarrow\text{a}\in\text{A}\text{ and b}\in\text{B}\ ...(\text{i})$
Now,
$(\text{a, b})\in\text{A}\times\text{B}$
$\Rightarrow(\text{a},\text{ b})\in\text{C}\times\text{D}$ $\big[\because\text{ A}\times\text{B}\subseteq\text{C}\times\text{D}\big]$
$\Rightarrow\text{a}\in\text{C and b}\in\text{D}\ ...(\text{ii})$
$\therefore\ \text{a}\in\text{A}$
$\Rightarrow\text{a}\in\text{C}$ [Using (i) and (ii)]
$\Rightarrow\text{A}\subseteq\text{C}$
and,
$\text{b}\in\text{B}$
$\Rightarrow\text{b}\in\text{D}$
$\Rightarrow\text{B}\subseteq\text{D}$
Hence, proved.

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 Relations→Relations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{6}}}\frac{\cot^2\text{x}-3}{\text{cosec x}-2}$
→
Find the equation of the parabola, if The focus is at $(0, -3)$ and the vertex is at $(-1, -3)$.
→
Prove that:
$(\text{A}\cup\text{B})\times\text{C}=(\text{A}\times\text{C})\cup(\text{B}\times\text{C})$
→
From the prices of shares X and Y below, find out which is more stable in value:
X 35 54 52 53 56 58 52 50 51 49
Y 108 107 105 105 106 107 104 103 104 101
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^4-3\text{x}^3+2}{\text{x}^3-5\text{x}^2+3\text{x}+1}$
→
Prove that: $\frac{\sin\text{(A-B)}}{\sin\text{A}\sin\text{B}}+\frac{\sin\text{(B-C)}}{\sin\text{B}\sin\text{C}}+\frac{\sin\text{(C-A)}}{\sin\text{C}\sin\text{A}}=0$
→
At the foot of a mountain, the elevation of it summit is 45°; after ascending 1000m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.
→
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. $36x^2 + 4y^2 = 144$
→
The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the values of m and c.
→
Let r and n be positive integers such that 1 < r < n. Then prove the following: ${^\text{n}\text{C}}_{\text{r}}+2\ {^\text{n}\text{C}}_{\text{r}-1}+{^\text{n}\text{C}}_{\text{r}-2}={^\text{n+2}\text{C}}_{\text{r}}$
→