Binary Relations


















What's a Binary Relation?

	A representation of the relationships between members of two sets

	A Binary Relation from A to B is a set of pairs,
	    where the first element of each pair comes from A
	    and the second element comes from B

	A subset of the Cartesian Product of two sets


Examples of Binary Relations

	The 'cousins' relation defined on a set of people.

	  cousins = { (Jim, Bob), (Bob, Jim), (Ann, Sue), (Sue, Ann) }

	The 'equals' relation defined on the set of natural numbers.

	  equals = { (1,1), (2,2), (3,3), ... }

	The 'enroll' relation from a set of people to a set of courses.

	  enroll = { (Bob, cs235), (Bob, cs236), (Ann, cs235), (Jim, cs236) }

	A relation with no obvious description.

	  R = { (1,1), (1,2), (2,2) }


What's the domain of a Binary Relation?

	The set from which the first element of each pair is taken.

What's the codomain of a Binary Relation?

	The set from which the second element of each pair is taken.


















Give the matrix or table representation for the relation.

	1. row for each domain value
	2. column for each codomain value
	3. entry is 1 when the pair is in the relation
	4. entry is 0 when the pair is not in the relation

	{ (B, 5), (B, 6), (A, 5), (J, 6) }


















Give the graph representation for the relation.

	1. node for each domain value
	2. node for each codomain value
	3. directed edge from x to y if (x,y) is in the relation

	{ (B, 5), (B, 6), (A, 5), (J, 6) }