Download App

Relations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations5 Marks
Question
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
$\text{A}\times(\text{B}\cup\text{C})=(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$
✓

Answer

We have,
$\text{A}=\{1,2,3\}\times\{4\}$
$\therefore\ \text{B}\cup\text{C}=\{4\}\cup\{5\}=\{4,5\}$
$\therefore\ \text{A}\times(\text{B}\cup\text{C})=\{1,2,3\}\times\{4,5\}$
$\Rightarrow\text{A}\times(\text{B}\cup\text{C})=\{(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)\}\ ...(\text{i}) $
Now,
$\text{A}\times\text{B}=\{1, 2, 3\}\times\{4\}$
$=\{(1, 4), (2, 4), (3, 4)\}$
and, $\text{A}\times\text{C}=\{1,2,3\}\times\{5\}$
$=\{(1, 5) , (2, 5), (3, 5)\}$
$\therefore\ (\text{A}\times\text{B})\cup(\text{A}\times\text{C})=\{(1, 4), (2, 4), (3, 4)\} \cup\{(1, 5), (2, 5), (3, 5)\}$
$\Rightarrow(\text{A}\times\text{B})\cup(\text{A}\times\text{C})=\{(1,4), (1,5), (2, 4), (2, 5), (3, 4), (3, 5)\}\ ...(\text{ii})$
From equation (i) and (ii), we get
$\text{A}\times (\text{B}\cup\text{C})=(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$
Hence verified.

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 Relations→Relations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Reduce each of the following expressions to the sine and cosin of a single expression:
$\sqrt{3}\sin\text{x}-\cos\text{x}$
→
Prove that:
$\frac{\sin\text{A}+\sin\text{B}}{\sin\text{A}-\sin\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big)\cot\Big(\frac{\text{A}-\text{B}}{2}\Big)$
→
Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos2\text{x}$ and $\text{y}=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)$
→
Prove the following identities:
$\frac{1−\sin\text{x}\cos\text{x}}{\cos\text{x}(\sec\text{x}−\text{cosec}\text{x})}\cdot\frac{\sin^2\text{x}−\cos^2\text{x}}{\sin^3\text{x}\cos^3\text{x}}=\sin\text{x}$
→
If $\sin\alpha+\sin\beta=\text{a}$ and $\cos\alpha+\cos\beta=\text{b},$ show that
$\sin(\alpha+\beta)=\frac{2\text{ab}}{\text{a}^2+\text{b}^2}$
→
If $\Big(\frac{1-\text{i}}{1+\text{i}}\Big)^{100}=\text{a}+\text{ib},$ find (a, b).
→
Let f = {(2, 4), (5, 6), (8, – 1), (10, – 3)}
g = {(2, 5), (7, 1), (8, 4), (10, 13), (11, 5)}
be two real functions. Then Match the following:
Column IColumn II
(a)$​​\text{f}-\text{g}$(i)$\Big\{\Big(2, \frac{4}{5}\Big), \Big(8, \frac{-1}{4}\Big), \Big(10, \frac{-3}{13}\Big)\Big\}$
(b)$\text{f}+\text{g}$(ii)$\{(2, 20), (8, -4), (10, -39)\}$
(c)$\text{f}\times\text{g}$(iii)$\{(2, 1), (8, -5), (10, -16)\}$
(d)$\frac{\text{f}}{\text{g}}$(iv)$\{(2, 9), (8, 3), (10, 10)\}$
→
Find the equation of the circle which passes through the points $(2, 3)$ and $(4,5)$ and the centre lies on the straight line $y - 4x + 3 = 0$
→
If $A =\{p, q, r, s\}, B =\{q, s, u\}$ and $C =\{r, s, t, u\}$, then prove the following :
(i) $(A-B) \cup(A-C)=A-(B \cap C)$
(ii) $A \cap(B \cup C)=(A \cap B) \cup(A \cap C)$
(iii) $A \cup(B \cap C)=(A \cup B) \cap(A \cup C)$
→
Prove the following identities:
$(1+\tan\alpha\tan\beta)^2+(\tan\alpha-\tan\beta)^2=\sec^2\alpha\sec^2\beta$
→