Okay, let me see if I can make this clear, found some trouble in an algebra book I'm reading, perhaps someone can explain how to solve that problem, this is in the Set Theory part, very basic, at the very start, I can't move forward until I get this one right. So, here it goes:
the book states:
A relation in a set A is defined by all the possible parts of A^2
beeing A^2 the cartesian product A*A, and parts of it all the possible subsets(including empty set and the same set)
Define relations of equivalence in a set with 2 elements, beeing a relation of equivalence part of A^2, that is defined by, symbolizing ? as such relation:
Reflexive: for all x that belongs to A: x?x
Symmetric: x?y -> y?x
Transitive: x?y, y?z -> x?z
I´m really boggled down on the transitive property on a set with 2 elements, according to this book...
the book states:
A relation in a set A is defined by all the possible parts of A^2
beeing A^2 the cartesian product A*A, and parts of it all the possible subsets(including empty set and the same set)
Define relations of equivalence in a set with 2 elements, beeing a relation of equivalence part of A^2, that is defined by, symbolizing ? as such relation:
Reflexive: for all x that belongs to A: x?x
Symmetric: x?y -> y?x
Transitive: x?y, y?z -> x?z
I´m really boggled down on the transitive property on a set with 2 elements, according to this book...
