Consider the following four relations on the set {1,2,3}

R1 = {(1,1), (1,3), (2,2), (3,1)}

R2 = {(1,1), (2,2), (3,1), (3,3)}

R3 = {(1,2), (2,1), (3,3)}

R4 = {(1,3),(2,3)}

Which one's are transitive? Im not getting the idea behind it.

Is if A,B and B,A then A,C

R2 and R4 is transitive in the book but I do not see why.

Isn't R1 transitive? the book says no.

(1,3) = A,B (3,1) = B,C then (1,1) = A,C?? Please explain. Thanks in advance.