Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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# Write the Following Relations as Sets of Ordered Pairs and Find Which of Them Are Functions:(C) {(X, Y) : X + Y = 3, X, Y, ∈ [0, 1, 2, 3]} - Mathematics

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

{(xy) : x + y = 3, xy, ∈ [0, 1, 2, 3]}

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#### Solution

Given:
{(xy) : x + y = 3, xy, ∈ [0, 1, 2, 3]}
x + y = 3
∴ y = 3 – x
On substituting x = 0,1, 2, 3 in y, we get:
y = 3, 2, 1, 0, respectively.
∴ R = {(0, 3), (1, 2), (2, 1), (3, 0)}
Hence, we observe that each element of the given set has appeared as the first component in one and only one ordered pair in R . So, R is a function in the given set.

Concept: Sets - Ordered Pairs
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.1 | Q 8.3 | Page 8
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