14a-Orders-and-Equivalences

14a-Orders-and-Equivalences - Equivalences Introduction...

This preview shows pages 1–6. Sign up to view the full content.

Equivalences Discrete Mathematics

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Mathematics – Equivalences 14-2 Previous Lecture Cartesian products of two and more sets Cardinality and other properties of Cartesian products Binary, ternary and k-ary relations Describing binary relations
Discrete Mathematics – Equivalences 14-3 Properties of Binary Relations – Reflexivity From now on we consider only binary relations from a set A to the same set A. That is such relations are subsets of A × A. A binary relation R A × is said to be reflexive if (a,a) R for all a A. (a,b) R Z × Z if and only if a b This relation is reflexive, because a a for all a Z Matrix: 1’s on the diagonal Graph: Loops at every vertex

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Mathematics – Equivalences 14-4 Properties of Binary Relations – Symmetricity A binary relation R A × A is said to be symmetric if, for any a,b A, if (a,b) R then (b,a) R. The relation Brotherhood (`x is a brother of y’) on the set of men is symmetric, because if a is a brother of b then b is a brother of a Matrix: Matrix is symmetric w.r.t. the diagonal Graph: Graph is symmetric
Discrete Mathematics – Equivalences 14-5 Properties of Binary Relations – Transitivity A binary relation R A × A is said to be transitive if, for any a,b,c A, if (a,b) R and (b,c) R

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 14

14a-Orders-and-Equivalences - Equivalences Introduction...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online