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Army Group X Practice Set 4

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Question : 46 of 70

Marks: +1, -0

What is the nature of relation

R

R

R=[(x,y):2x+y=41,x,y\in N]

reflective
symmetric
transitive
None of these

Solution:

Given,

R=\{(x,y):2x+y=41,x,y\in N\}

\Rightarrow R=

(1,39),(2,37),(3,35),(4,33),

(5,31),(6,29),(7,27),(8,25),

(9,23),(10,21),(11,19),(12,17),

(13,15),(14,13),(15,11),(16,9),

(17,7),(18,5),(19,3),(20,1)

Here,

(a,a) \in R

so, R is not reflexive.

\therefore (a,b)\in R\Rightarrow (b,a)\notin R,

so

R

is not symmetric and

(a,b)\in R\Rightarrow (b,a)\in R

(a,c)\notin R,\text{ so }R

is not transitive.

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