15 - IOrders and Equivalences ntroduction Discrete...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Introduction Orders and Equivalences Discrete Mathematics Andrei Bulatov
Background image of page 1

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

View Full DocumentRight Arrow Icon
Discrete Mathematics – Orders and Equivalences 15-2 Previous Lecture Properties of binary relations Equivalence relations s reflexivity s symmetricity s transitivity s anti-symmetricity
Background image of page 2
Discrete Mathematics – Orders and Equivalences 15-3 Properties of binary relations Reflexivity A binary relation R A × A is said to be reflexive if (a,a) R for all a A. 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. 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 then (a,c) R. Anti-symmetricity A binary relation R A × A is said to be anti-symmetric if, for any a,b A, if (a,b) R and (b,a) R then a =b.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Discrete Mathematics – Orders and Equivalences 15-4 Equivalence relations A binary relation R on a set A is said to be an equivalence relations if it is reflexive, symmetric, and transitive. Let R People × People. Pair (a,b) R if and only if a and b are of the same age. Equivalence classes. Take a A. The set C(a) = { b | (a,b) R} is called the equivalence class of a. For example,
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/14/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

Page1 / 13

15 - IOrders and Equivalences ntroduction Discrete...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online