Let N denote the set of all natural numbers. | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Here,

${R_1} = \left\{ {\left( {x,y} ight) \in N 	imes N:2x + y = 10} ight\}$

${R_2} = \left\{ {\left( {x,y} ight) \in N 	imes N:x + 2y

Vedclass · Accepted Answer

Range of  $R_2$ is $\{1, 2, 3, 4\}$

Vedclass · Answer

Here,

${R_1} = \left\{ {\left( {x,y} ight) \in N 	imes N:2x + y = 10} ight\}$

${R_2} = \left\{ {\left( {x,y} ight) \in N 	imes N:x + 2y = 10} ight\}$

For ${R_1};2x + y = 10$ and $x,y \in N$

So, possible values for $x$ and $y$ are:

$x = 1,y = 8$ i.e. $(1,8);$

$x = 2,y = 6\,$ i.e. $(2,6);$

$x = 3,y = 4$ i.e. $\,(3,4)$ and 

$x = 4,y = 2\,$ i.e. $(4,2)$.

${R_1} = \left\{ {(1,8),(2,6),(3,4),(4,2)} ight\}$

Therefore, Range of ${R_1}$ is $\left\{ {2,4,6,8} ight\}$

${R_1}$ is not symmetric

Also,${R_1}$ is not transitive because

$(3,4),(4,2) \in {R_1}$ but $\,(3,2) 
otin {R_1}$

Thus, options $A,B$ and $D$ are incorrect.

For ${R_2};x + 2y = 10$ and $x,y \in N$

So, possible values for $x$ and $y$ are:

$x = 8,y = 1\,$i.e.$\,(8,1);$

$x = 6,y = 2$i.e.$(6,2);$

$x = 4,y = 3$i.e.$(4,3)$ and 

$x = 2,y = 4$i.e.$(2,4)$

${R_2} = \left\{ {(8,1),(6,2),(4,3),(2,4)} ight\}$

Therefore, Range of ${R_2}$ is $\left\{ {1,2,3,4} ight\}$

 ${R_2}$ is not symmetric and transitive.

Let $N$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_1 = \{(x,y) \in N \times N : 2x + y= 10\}$ and $R_2 = \{(x,y) \in N\times N : x+ 2y= 10\} $. Then

Similar Questions

How many reflexive relation are there on a set ' with $3$ elements

Let $n(A) = n$. Then the number of all relations on $A$ is

The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is

Show that the relation $\mathrm{R}$ in the set $\mathrm{Z}$ of integers given by $\mathrm{R} =\{(\mathrm{a}, \mathrm{b}): 2$ divides $\mathrm{a}-\mathrm{b}\}$ is an equivalence relation.

If $R = \{(6, 6), (9, 9), (6, 12), (12, 12), (12,6)\}$ is a relation on set $A = \{3, 6, 9, 12\}$ , then relation $R$ is