I'm looking at a True or False question in my book and it is very close to identical to the definition of the transitive property in the book, though this answer is False. If someone could explain to me why this is False, I would be very appreciative.
Here's the True or False Statement:
Let R be a binary relation on a set A. If there exist a,b,c within A such that (a,b) within R, (b,c) within R, and (a,c) within R, then R must be transitive.
Here's the definition from the book:
A binary relation R on a set A is transitive if and only if
if a,b,c is within A, and both (a,b) and (b,c) are in R, then (a,c) is within R