First slide

Relations XII

Question

Let R be a relation on the set N be defined by $\{(x, y) | x, y \in N, 2 x + y = 41\} .$ Then R is

Easy

A

Reflexive
B

Symmetric
C

Transitive
D

None of these

Solution

On the set N of natural numbers,
$R = \{(x, y) : x, y \in N, 2 x + y = 41\} .$
Since $(1, 1) \notin R as 2.1 + 1 = 3 \neq 41 .$ So, R is not reflexive. $(1, 39) \in R but (39, 1) \notin R .$
So R is not symmetric $(20, 1)$ , $(1, 39) \in R . But (20, 39) \notin R,$ So R is not transitive.

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