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

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

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