My teacher in discrete math is very meticulous about how we motivate our answers in the course.
For instance, the exercise:
Put A={1,2,3} and form the relation R on A by putting R= {(1, 1),(2, 2),(3, 3),(1, 2),(2, 3),(3, 1)}.
Investigate if R is: reflexive and symmetric. If the relation has a property, give proof for it and if the relation doesn't have the property, prove it.
My answer:
It is reflexive: A is {1,2,3} and in R there is (1,1), (2,2), and (3,3). Every element in A exists as a pair in R, therefore it is reflexive.
It is not symmetric, as in R there is (1,2), (2,3) and (3,1), but there is no (2,1), (3,2) or (1,3) respectively. For symmetry, every pair in R would have needed a reserve pair.
Am I correct in my motivations or is there a better way to motivate myself?
It is reflexive. (3,3) is there in R. Your argument on non-symmetry is correct.