Question

Let R be a relation on I ( the sets of integers) defined as m R n ( m, n$\in$I ) iff m $\le$ n. Check R for reflexivity, symmetry, transitivity and anti-symmetry.

Answer 1

R, $\ne$ S, T, Anti-symmetric.
R is reflexive since x = x for all x $\in$ I.
[ Note that by definition of R, xRy iff either x= y or x < y] R is not symmetric. For example 1 R 2 since 1 < 2. But 2 (~R) a since 2 > 1.
R is transitive since m $\le$ n and n $\le$ p $\to$ m $\le$ p,
R is anti-symmetric since
m $\le$ n and n $\le$ m $\to$ m = n.