Let A -2-3-4-6 and R - x - y - y - x 2- x - x - y - A is a relation on A- then write R as set of ordered pairs-

Given, A={2, 3, 4, 6} and R={(x,y):y = x^2 x; x,y∈ A} Putting value of elements of A for R x=2 ⇒ y=2 x=3 ⇒ y=6 x=4 ⇒ y=12 x=6 ⇒ y=30 But, y=12,30 ∉A So, th ...

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Standard XII

Mathematics

Relation Definition

Let A =2,3,4,...

Question

Let $A = {2, 3, 4, 6}$ and $R = {(x, y) : y = x^{2} - x; x, y \in A}$ is a relation on $A$ , then write $R$ as set of ordered pairs ?

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Solution

Given, $A = {2, 3, 4, 6}$ and $R = {(x, y) : y = x^{2} - x; x, y \in A}$

Putting value of elements of $A$ for $R$
$x = 2 \Rightarrow y = 2 x = 3 \Rightarrow y = 6 x = 4 \Rightarrow y = 12 x = 6 \Rightarrow y = 30$
But, $y = 12, 30 \notin A$

So, the set of elements for $R$ is
$R = {(2, 2), (3, 6)}$

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Let A={2, 3, 4, 6} and R={(x,y):y = x2−x; x,y∈A} is a relation on A, then write R as set of ordered pairs ?

Given, A={2, 3, 4, 6} and R={(x,y):y = x2−x; x,y∈A} Putting value of elements of A for R x=2⇒y=2x=3⇒y=6x=4⇒y=12x=6⇒y=30 But, y=12,30∉A So, the set of elements for R is R={(2,2),(3,6)}

Let $A = {2, 3, 4, 6}$ and $R = {(x, y) : y = x^{2} - x; x, y \in A}$ is a relation on $A$ , then write $R$ as set of ordered pairs ?