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:

A, B and D only

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