Show that the relation R in R defined as R = {(a,b) : a$\le$b}, is reflexive and transitive but not symmetric.

Check if reflexive:

(a,a) $\in$ R a$\le$a

∴ R is reflexive



Check if transitive:

(a,b) $\in$ R a$\le$b

(b,c) $\in$ R b$\le$c

(a,c) $\in$ R a$\le$c

∴ R is transitive



Check if symmetric:

(a,b) $\in$ R a$\le$b

(b,a) $\notin$ R b not $\le$a

e.g. (1,2) $\in$ R 1$\le$2

(2,1) $\notin$ R 2 not $\le$1

∴ R is not symmetric