Define a relation R on A that is:

not reflexive, not symmetric, transitive

my ans: {(1,2), (2,3), (1,3)}

Can it be only three elements?

not reflexive, symmetric, transitive

my ans: {(1,2), (2,1), (2,3), (3,2), (1,3), (3,1)}

I read that each of the three property should be independent to each other, but in this case if the relation is transitive, (1,2) and (2,1) will imply (1,1) is in R. But it is given that R is not reflexive. What should be the right answer?

reflexive, symmetric, not transitive

my ans: {(1,1), (2,2), (3,3)}

Correct? Same as the relation that is reflexive, not symmetric and not transitive?

not reflexive, not symmetric, not transitive

my ans: {(1,2), (1,3)}

Correct?

reflexive, symmetric, transitive

my ans: {(1,1), (2,2), (3,3), (1,2), (2,1), (1,3), (3,1), (2,3), (3,2)}

Correct?