Tag: relations

Questions Related to relations

If $A$ and $B$ are two sets containing four and two elements, respectively. Then the number of subsets of the set $A\times B$ each having at least three elements is

  1. $219$

  2. $256$

  3. $275$

  4. $510$


Correct Option: A
Explanation:

$A=\left{a,b,c,d\right}$

$B=\left{x,y\right}$
$A\times B=2\times 4=8$ Elements.
Total number of subsets of $A\times B$ having $3$ or more elements $=2^8=256$
$\Rightarrow 256-(1$ null set $+$ $8$ singleton set $+$ $^8e _2$having $2$ elements$)$
$=256-1-8-28$
$=219$

If $A = {1, 2 }$ and $B = {3, 4}$ then find $A \times B$

  1. $A \times B = {(1,3),(1,2),(2,3),(2,4)}$

  2. $A \times B = {(1,3),(1,4),(2,3),(2,4)}$

  3. $A \times B = {(1,3),(1,4),(2,1),(2,4)}$

  4. $A \times B = {(1,3),(1,4),(2,3),(2,1)}$


Correct Option: B
Explanation:

$A\times B = {(1,3),(1,4),(2,3),(2,4)}$.

If $x$ co-ordinate of a point is $2$ and $y$ co-ordinate is $0$, then ordered pair for its coordinate on $XY$ plane is

  1. $(0, 0)$

  2. $(2, 2)$

  3. $(0, 2)$

  4. $(2, 0)$


Correct Option: D
Explanation:

Ordered pair for co-ordinate of a point in $XY$ plane is written as $(x, y).$

So, option D is correct.

What is general representation of ordered pair for two variables $a$ and $b$?

  1. $a, b$

  2. $(a, b)$

  3. $(a), b$

  4. $a, (b)$


Correct Option: B
Explanation:

An ordered pair is written in the form $(x-$coordinate, $y-$coordinate$)$.

If $a$ and $b$ are two variables and $(a, b)=(b, a)$, then 

  1. $a = 0$

  2. $b = 0$

  3. $a = b$

  4. $\displaystyle a\pm b$


Correct Option: C
Explanation:

 $(a, b) = (b, a)$ only if $a = b.$.

So, option C is correct.

If $x$ and $y$ co-ordinate of a point is $(3, 10)$, then $y$ co-ordinate is

  1. $0$

  2. $3$

  3. $10$

  4. None of the above


Correct Option: C
Explanation:

$y$ coordinate will be second entry in ordered pair.

So, option C is correct.

If $x$ and $y$ coordinate of a point is $(3, 10)$, then the $x$ co-ordinate is

  1. $0$

  2. $3$

  3. $10$

  4. None of the above


Correct Option: B
Explanation:

Here, $x$ co-ordinate will be the first entry in ordered pair.

So, option B is correct.

If ordered pair $(a, b)$ is given as $(-2, 0)$, then $a =$

  1. $-2$

  2. $0$

  3. $2$

  4. None of the above


Correct Option: A
Explanation:

$a$ will be first entry in ordered pair $(a, b).$

So, option A is correct.

If $y$ is second entry and $x$ is first entry then its ordered pair will be ............

  1. $(x, y)$

  2. $(y, y)$

  3. $(y, x)$

  4. None of the above


Correct Option: A
Explanation:

If $x$ is first entry and $y$ is second, then its ordered pair will be $(x, y)$.


So, option A is correct.

Identify the first component of an ordered pair $(2, 1)$.

  1. $1$

  2. $2$

  3. $-1$

  4. $0$


Correct Option: B
Explanation:

In an ordered pair $(x,y)$, the first component is $x$ and the second component is $y$.

Therefore, in an ordered pair $(2,1)$, the first component is $2$.