First slide

Relations XII

Question

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

Moderate

A

Reflex
B

Symmetric
C

Transitive
D

None of these

Solution

$R e l a t i o n R = \{(1, 39), (2, 37), . . ., (20, 1)\}$
$T h i s i s n o t r e f l e x i v e, b e c a u s e (1, 1) i s n o t a n e l e m e n t i n t h e r e l a t i o n R$
$T h i s i s n o t s y m m e t r i c b e c a u s e (1, 39) i s a n e l e m e n t b u t (39, 1) i s n o t a n e l e m e n t$
$(19, 3) a n d (3, 35) a r e e l e m e n t s o f R b u t (19, 35) i s n o t a n e l e m e n t o f R$
$S o R i s n o t t r a n s i t i v e$
$T h e r e f o r e, t h e r e l a t i o n i s n o t r e f l e x i v e, n o t s y m m e t r i c a n d n o t t r a n s i t i v e$

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