Question

Let $A=\{0,1,2,3\}$ and $R$ be relation on $A$ defined as $R=\{(0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)\}$
Is $R$ reflexive, symmetric, transitive?

Answer 1

R is reflexive relation over set A as every element of A is related to itself in R .

R is also a symmetric relation as for a,b in A , if (a,b) is in R, (b,a) is also in R.

R is not a transitive relation as (1,0) is in R and (0,3) is also in R, but (1,3) is not in R.