Ordered pairs, relations and equivalence
Mark A × B as points, pick out a relation, reverse it to get the inverse and see why "same remainder" is an equivalence relation.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- Afghanistan: grade 10
- Palestine: grade 9
Guide
An ordered pair (a, b) has a first and a second number and the order matters. The Cartesian product A×B is the set of all pairs with the first number from A and the second from B. On the plane it is a grid of points.
A relation from A to B is a part (a subset) of A×B. Its inverse R−1 has every pair reversed.
A relation on one set is an equivalence relation when it is reflexive (every x is related to itself), symmetric (x ~ y means y ~ x) and transitive (x ~ y and y ~ z mean x ~ z). It splits the set into classes.