Questions
Let R be the relation on the set of all real numbers defined
a
Reflexive and symmetric
b
Symmetric only
c
Transitive only
d
Anti-symmetric only
detailed solution
Correct option is A
|a−a|=0<1∴aRa∀a∈RTherefore, R is reflexive. Again aRb⇒|a−b|≤1 and b−a∣≤1⇒bRaTherefore, R is symmetric. Again 1R12 and 12R1 but 12≠1Therefore, R is not anti-symmetric. Further, 1R2 and 2R3 but 1R3,[∵|1−3|=2>1]Therefore, R is not transitive.Talk to our academic expert!
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