Write the relations as sets of ordered pairs x-y - y - 3x- x-1-2-3- y-3-6-9-12

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Standard XII

Mathematics

Definition of Relations

Write the rel...

Question

Write the relations as sets of ordered pairs ${(x, y) : y = 3 x, x \in {1, 2, 3}, y \in {3, 6, 9, 12}}$

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Solution

${(x, y) : y = 3 x, x \in {1, 2, 3}, y \in {3, 6, 9, 12}}$

When $x = 1$ , we have $y = 3 (1) = 3$

When $x = 2$ , we have $y = 3 (2) = 6$

When $x = 3$ we have $y = 3 (3) = 9$

Thus, $R = {(1, 3), (2, 6), (3, 9)}$

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Similar questions

Q. Write the following relations as sets of ordered pairs and find which of them are functions:

(a) {(x, y) : y = 3x, x ∈ {1, 2, 3}, y ∈ [3,6, 9, 12]}
(b) {(x, y) : y > x + 1, x = 1, 2 and y = 2, 4, 6}
(c) {(x, y) : x + y = 3, x, y, ∈ [0, 1, 2, 3]}

Write the following relations as sets of ordered pairs and find which of them are functions :
(i) ${(x, y) : y = 3 x, x ϵ (1, 2, 3), y ϵ (3, 6, 9, 12)}$
(ii) ${(x, y) : y > x + 1, x = 1, 2}$ and y = 2, 4, 6
(iii) ${(x, y) : x + y = 3, x, y ϵ {0, 1, 2, 3}}$

Q. Express

R = (x, y), y = 3 x, x \in (1, 2, 3) and y \in (3, 6, 9, 12)

as a set of ordered pair.

Q. 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 ?

Q. A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.

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Write the relations as sets of ordered pairs {(x,y):y=3x,x∈{1,2,3},y∈{3,6,9,12}}

{(x,y):y=3x,x∈{1,2,3},y∈{3,6,9,12}}When x=1, we have y=3(1)=3When x=2, we have y=3(2)=6When x=3 we have y=3(3)=9Thus, R={(1,3),(2,6),(3,9)}

Write the relations as sets of ordered pairs ${(x, y) : y = 3 x, x \in {1, 2, 3}, y \in {3, 6, 9, 12}}$

${(x, y) : y = 3 x, x \in {1, 2, 3}, y \in {3, 6, 9, 12}}$

When $x = 1$ , we have $y = 3 (1) = 3$

When $x = 2$ , we have $y = 3 (2) = 6$

When $x = 3$ we have $y = 3 (3) = 9$

Thus, $R = {(1, 3), (2, 6), (3, 9)}$