Is the following reflexive, symmetric, and/or transitive: A = {1,2}; R = {(1,2)}?

Question

If you can help me understand these 3 terms that would also be very much appreciated.

Answer 1

Reflexive: this means that for all x∈A, (x, x)∈R. Note that (1, 1) and (2, 2) do not appear in the relation, so R is not reflexive.
Symmetric: this means that if (x, y)∈R, (y, x)∈R. Note that (1, 2) appears in the relation, but (2, 1) does not, so this relation is not symmetric.
Transitive: this means that if (x, y)∈R, and (y, z)∈R, (x, z)∈R. This relation IS transitive, but only vacuously so, since the transitivity comes from the fact that there _are_ no three distinct elements x, y and z such that (x, y)∈R and (x, z)∈R.