Question

Let A be a finite set and f a function from A to A. Prove That...

Let A be a finite set and f a function from A to A. Prove That f is one-to-one if and only if f is onto.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let A be a nonempty set. Prove that the set S(A) = {f : A →...
Let A be a nonempty set. Prove that the set S(A) = {f : A → A | f is one-to-one and onto } is a group under the operation of function composition.
Let A be a finite set and let f be a surjection from A to itself....
Let A be a finite set and let f be a surjection from A to itself. Show that f is an injection. Use Theorem 1, 2 and corollary 1. Theorem 1 : Let B be a finite set and let f be a function on B. Then f has a right inverse. In other words, there is a function g: A->B, where A=f[B], such that for each x in A, we have f(g(x)) = x. Theorem 2: A right inverse...
Let g be a function from set A to set B and f be a function...
Let g be a function from set A to set B and f be a function from set B to set C. Assume that f °g is one-to-one and function f is one-to-one. Using proof by contradiction, prove that function g must also be one-to-one (in all cases).
Let F = {A ⊆ Z : |A| < ∞} be the set of all finite...
Let F = {A ⊆ Z : |A| < ∞} be the set of all finite sets of integers. Let R be the relation on F defined by A R B if and only if |A| = |B|. (a) Prove or disprove: R is reflexive. (b) Prove or disprove: R is irreflexive. (c) Prove or disprove: R is symmetric. (d) Prove or disprove: R is antisymmetric. (e) Prove or disprove: R is transitive. (f) Is R an equivalence relation? Is...
Prove Cantor’s original result: for any nonempty set (whether finite or infinite), the cardinality of S...
Prove Cantor’s original result: for any nonempty set (whether finite or infinite), the cardinality of S is strictly less than that of its power set 2S . First show that there is a one-to-one (but not necessarily onto) map g from S to its power set. Next assume that there is a one-to-one and onto function f and show that this assumption leads to a contradiction by defining a new subset of S that cannot possibly be the image of...
Prove that a disjoint union of any finite set and any countably infinite set is countably...
Prove that a disjoint union of any finite set and any countably infinite set is countably infinite. Proof: Suppose A is any finite set, B is any countably infinite set, and A and B are disjoint. By definition of disjoint, A ∩ B = ∅ Then h is one-to-one because f and g are one-to one and A ∩ B = 0. Further, h is onto because f and g are onto and given any element x in A ∪...
Let A be a non-empty set and f: A ? A be a function. (a) Prove...
Let A be a non-empty set and f: A ? A be a function. (a) Prove that, if f is injective but not surjective (which means that the set A is infinite), then f has at least two different left inverses.
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
Let P be the set of all people, dead or alive. Consider the function f: P\longrightarrow...
Let P be the set of all people, dead or alive. Consider the function f: P\longrightarrow P where, if x is a person in P, then f(x) is the biological father of x. In order to make this a well-defined function, we will assume that everyone has one and only one biological father. Check all of the following statements that apply. E. The function $f$ is not 1-1 because there are some people who do not have children. F. The...
Let X be a non-empty finite set with |X| = n. Prove that the number of...
Let X be a non-empty finite set with |X| = n. Prove that the number of surjections from X to Y = {1, 2} is (2)^n− 2.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT