Question

Given sets A and B, what is the function f: A->B?

Answer #1

f: A→B be a function.

If each element in the codomain ‘ B‘ has at least one pre-image in the domain A that is, for every b ∈B there exists at least one element a ∈ A such that f(a) = b, then f is onto.

In other words range of f = B , for onto functions.

On the other hand if there exists at least one element in the codomain B which is not an image of any element in the domain A, then f is into.

Onto function is also called **Surjective
function** and a function which is both one-one and onto is
called **Bijective function.**

e.g. f : R->R where f(x) = sinx is into.

f : R−>R where f(x) = ax^{3} + b is onto where a ≠ 0
, b∈ R.

Given two sets A and B, the
intersection of these sets, denoted A ∩
B, is the set containing the elements that are in both
A and B. That is, A ∩ B =
{x : x ∈ A and x ∈
B}.
Two sets A and B are
disjoint if they have no elements in common. That
is, if A ∩ B = ∅.
Given two sets A and B, the union of
these sets, denoted A ∪ B,...

For the given grammar below, find the first and follow function
sets. Then, construct the parsing table. By using the LL(1) parser
and the parsing table, find if the given string “acfh” is accepted
or rejected.
S → aBDh
B → cC | ε
C → bC | ε
D → EF
E → g | ε
F → f | ε

Let A and B be nonempty sets. Prove that if f is an injection,
then f(A − B) = f(A) − f(B)

Let A and B be nonempty sets. Prove that if f is an injection,
then f(A − B) = f(A) − f(B)

Discrete Math
In this assignment, A, B and C represent sets, g is a function
from A to B, and f is a function from B to C, and h stands for f
composed with g, which goes from A to C.
a). Prove that if the first stage of this pipeline, g, fails to
be 1-1, then the entire pipeline, h can also not be 1-1. You can
prove this directly or contrapositively.
b). Prove that if the second...

Let A, B, C be sets and let f : A → B and g : f (A) → C be
one-to-one functions. Prove that their composition g ◦ f , defined
by g ◦ f (x) = g(f (x)), is also one-to-one.

2) Given sets A, B. Two sets are equivalent if there is a
bijection between them. Prove A x B is equivalent to B x A using
bijection

Given f(x) = x4 – 4x3, graph the nonlinear
function and answer the following:
a) What coordinates are the absolute minimum?
b) The function is concave downward for
c) The function is increasing for what values of X?
d) What are the X- intercepts?
e) What coordinates are the inflection point?

A function f(x) and interval [a,b] are given. Check if the Mean
Value Theorem can be applied to f on [a,b]. If so, find all values
c in [a,b] guaranteed by the Mean Value Theorem
Note, if the Mean Value Theorem does not apply, enter
DNE for the c value.
?(?)=11?^2−5?+5 on [−20,−19]
What does C=?

Let A, B be sets and f: A -> B. For any subsets X,Y subset of
A, X is a subset of Y iff f(x) is a subset of f(Y).
Prove your answer. If the statement is false indicate an
additional hypothesis the would make the statement true.

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