MATH 144 EXAM 2 & 3 QUESTIONS WITH VERIFIED ANSWERS,100%CORRECT

MATH 144 EXAM 2 & 3 QUESTIONS WITH
VERIFIED ANSWERS
R-¹. Contains all ordered pairs of R with their components exchanged (bra) --> (am)
for every pair in R - CORRECT ANSWER Inverse of a relation



a relation of ordered pairs (arc), a ∈ A, c ∈ C. Such that (am) and (back) ∈ F -
CORRECT ANSWER Composite of F and G


A relation R on set A is reflexive, symmetric, and transitive - CORRECT ANSWER
Equivalence Relation


The set of all elements of the base relation equivalent to a given element as
defined by the relation - CORRECT ANSWER Equivalence Class


A relation R on set A is reflexive, antisymmetric, and transitive - CORRECT ANSWER
Reflexive/Weak Partial Order


A relation R on a set A is irreflexive, transitive, and anti-symmetric - CORRECT
ANSWER Irreflexive/Strict Partial Order



A relation R on set A where all members of A, (a, a) ∉ R - CORRECT ANSWER
Irreflexive



Let R be a weak partial order on set A, a and b are comparable if a, b ∈ A and
either (a, b) ∈ R or (b, a) ∈ R (funky < symbol) - CORRECT ANSWER Comparable

, A weak partially-ordered relation R on set A is a total order if every pair of
elements a, b ∈ A are comparable. - CORRECT ANSWER Total Order


for f: X --> Y. X is the domain - CORRECT ANSWER Domain


for f: X --> Y. Y is the codomain - CORRECT ANSWER Codomain


for f(n) = p. p is the image of n - CORRECT ANSWER Image


for f(n) = p. N is the preimage of p - CORRECT ANSWER Preimage


The range of f is the set of all images of elements of X (not the same as codomain)
- CORRECT ANSWER Range



A relation from X to Y (denoted 'f: X --> Y') such that f(x) is fined ∀x ∈ X and for
each x in X there is one (XXY) ∈ f (one output for each input) - CORRECT ANSWER
Function


The largest integer <= n - CORRECT ANSWER Floor function


the smallest integer >= n - CORRECT ANSWER Ceiling function



for each y ∈ Y, F(x) = y for at most one member of X - CORRECT ANSWER Injective
(One - to - One)