Discrete Structure 2 Semi-Final Examination

A relation from A into B is any subset of A×B.

• Relation on a set

• Relation between two sets

• Composition of relation

A relation from a set A into itself is called a relation on A.

• Relation on a set

• Relation between two sets

• Composition of relation

R be a relation from a set A into a set B, and let’s be a relation from B into a set C.

• Relation on a set

• Relation between two sets

• Composition of relation

This relation as a graph, elements of A are called the vertices of the graph. They are typically represented by labeled points or small circles.

• Reflexive

• Antisymmetric

• Directed Graph

Let A be a set and let r be a relation on A. Then r is ____________________ if and only if whenever arb and a=b then bra is false.

• Reflexive

• Antisymmetric

• Directed Graph

Let A be a set and let r be a relation on A. Then r is ________________ if and only if ara for all a A

• Reflexive

• Antisymmetric

• Directed Graph

A relation on a set A that is reflexive, antisymmetric, and transitive is called a _______________________ on A. A set on which there is a partial ordering relation defined is called a ____________________________.

• Symmetric Relation

• Equivalence Relation

• Partial Ordering

Let r be a relation on a set A. r is ________________ if and only if whenever arb, it follows that bra.

• Symmetric Relation

• Equivalence Relation

• Partial Ordering

A relation r on a set A is called an __________________________ if and only if it is reflexive, symmetric, and transitive.

• Symmetric Relation

• Equivalence Relation

• Partial Ordering

What relation represent these entries of R as zero, .

• Adjacency Matrix

• Boolean Arithmetic

• Composition as Matrix Multiplication