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.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

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...
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 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.
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove...
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove that f is surjective (onto).
1. Let A = {1,2,3,4} and let F be the set of all functions f from...
1. Let A = {1,2,3,4} and let F be the set of all functions f from A to A. Prove or disprove each of the following statements. (a)For all functions f, g, h∈F, if f◦g=f◦h then g=h. (b)For all functions f, g, h∈F, iff◦g=f◦h and f is one-to-one then g=h. (c) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f then g = h. (d) For all functions f, g, h ∈...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT