Questions
Let a relation R on the set N of natural number be defined as If and only If for all, and the relation is
a
reflexive
b
symmetric
c
transitive
d
an equivalence relation
detailed solution
Correct option is A
we have,R={(x,y);x2−4xy+3y2=0,x,y∈NLet x∈N,x2−4x⋅x+3x2=0∴ (x,x)∈RR is reflexivewe have, (3)2−4(3)(1)+3(1)2=9−12+3=0 (3,1)∈RAlso,(1)2−4(1)(3)+3(3)2=1−12+27=16≠0(3)2−4(3)(1)+3(1)2=0now, (9,1)∈Rif(9)2−4(9)(1)+3(1)2=0i.e 48≠0which is not so (9,3),(3,1)∈Rand(9,1)∉R∴R is not transitive.Talk to our academic expert!
Similar Questions
Let R be a reflexive relation on a finite set A having elements, and let there be m ordered pairs in R. Then
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