First slide

Functions (XII)

Question

In the set $X = \{a, b, c, d\}$ , which of the following functions in X ?

Moderate

A

$R_{1} = {(b, a) (a, b), (c, d), (a, c)}$
B

$R_{2} = {(a, d) (d, c), (b, b), (c, c)}$
C

$R_{3} = {(a, b) (b, c), (c, d), (b, d)}$
D

$R_{4} = {(a, a) (b, b), (c, c), (a, d)}$

Solution

$X = {a, b, c, d}$
$R_{1} = \{(b, a), (a, b), (c, d), (a, c)\} (a, b) \in R_{1} and (a, c) \in R, ∴ R_{1} is not a function . R_{2} = {(a, d), (d, c), (b, b), (c, c)}$
Hence, R₂ is a function.

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