Math 199 - Final Exam with verified
solutions 2024
Onto Function
F is onto if and only if for all y that is an element Y, there exists an element x
in X such that f(x) = y.
One-to-One Function
A function from the set X to the set Y is one-to-one provided that if f(x1) =
f(x2), then x1 = x2.
Direct Image
Let f: X--> Y and A⊆X. The direct image of A, under f, is the set f(A) = {y∈Y |
there exists a∈A s.t. f(A) = Y}.
Inverse Image
Let f: X-->Y and V⊆Y. The inverse image of V under f is the set: f^-1(V)={a∈X |
f(a)∈V}.
Reflexive
R is reflexive if and only if for all a∈X, aRa
Symmetric
R is symmetric if and only if for all a, b∈X, if aRb, then bRa.
Transitive
R is transitive if and only if for all a, b, and c that are elements of X, if aRb and
bRc, then aRc.
Equivalence Relation
R is an equivalence relation if and only if R is reflexive, symmetric, and
transitive.
Equivalence Class
