Equivalence Relations

Question 1

relation

Answer 1

set of ordered pairs
with the following properties :
1. reflexivity
2. symmetry
3. antisymmetry
4. transitivity

Question 2

equivalence relations

Answer 2

relation R is an equivalence relation on set X if it is reflective, symmetric and transitive ( denoted by ~ (tilde)) = is equivalent to

Question 3

partial orderings

Answer 3

A relation on X is a partial ordering on X if and only if it is reflective, antisymmetric and transitive ( denoted with ≤ )

Question 4

y≥x

Answer 4

is the inverse of the relation y≤ x

Question 5

x<y

Answer 5

x precedes y

Question 6

y>x

Answer 6

y succeeds x

Question 7

upper bound

Answer 7

A is said to be bounded above if and only if there exists x ∈ X such that a ≤ x for all a ∈ A

Question 8

lower bound

Answer 8

A is said to be bounded above if and only if there exists x ∈ X such that a ≥ x for all a ∈ A

Question 9

supremum

Answer 9

least upper bound

Question 10

Infinium

Answer 10

highest lower bound

Question 11

linear orderings

Answer 11

every pair of elements x and y in A is comparable under ≤. A linearly ordered set is also called a chain.