A={1,2,3}, find ordered pairs on A which satisfy
1) R1 is transitive
2) R2 is non-symmetric and non-antisymmetric
At first, I thought 1) is a simple question, and the result is {<1,2>,<2,3>,<1,3>}.
However, the answer tells I am wrong.
As for 2), I am not sure if or not the ordered pairs exist on A?
Any help will be greatly appreciated!
[Update]
Really thanks for Scott's help.
1) The answer for the first question is {<1,2>,<2,1>,<1,1>,<2,2>,<3,3>}
However,I don't know why the answer is above.
2)
Find a non-symmetric relation on A: {<1,2>}
Find a non-antisymmetric relation on A: {<1,3>,<3,1>}
so R2 is {<1,2>,<1,3>,<3,1>}
I am not sure if it is right, because {<1,3>,<3,1>} is symmetric.