Let R be a relation on the set of integers given by $(x, y) \in R ⇔ |x-y| ≤ 1$. Then R is
A. Reflexive relation
B. Symmetric relation
C. Transitive relation
D. R is not a function
E. empty relation
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - A, B and D only
for every $x∈z$ (integer set)
$|x-x|=0≤1$
$(x,y)∈R$ R is reflexive
$⇒|x-y|≤1,⇒|y-x|≤1, ⇒(y,x)∈R$
R is symmetric
R is not transitive as $(1, 2) ∈R, (2,3)∈R$ but $(1,3)∉R$
for every $x∈z$
R is not defined
R is not a function