Question

Let n ∈ N and f : [n] → [n] a function. Prove that f is...

Let n ∈ N and f : [n] → [n] a function. Prove that f is a surjection if and only if f is an injection.

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 f : Z → N be function. a. Prove or disprove: f is not...
. Let f : Z → N be function. a. Prove or disprove: f is not strictly increasing. b. Prove or disprove: f is not strictly decreasing.
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g...
3. Let N denote the nonnegative integers, and Z denote the integers. Define the function g : N→Z defined by g(k) = k/2 for even k and g(k) = −(k + 1)/2 for odd k. Prove that g is a bijection. (a) Prove that g is a function. (b) Prove that g is an injection . (c) Prove that g is a surjection.
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 f(n) be a negligible function and k a positive integer. Prove the following: (a) f(√n)...
Let f(n) be a negligible function and k a positive integer. Prove the following: (a) f(√n) is negligible. (b) f(n/k) is negligible. (c) f(n^(1/k)) is negligible.
Let f be a function from the set of students in a discrete mathematics class to...
Let f be a function from the set of students in a discrete mathematics class to the set of all possible final grades. (a) Under what conditions is f an injection? (b) Under what conditions is f a surjection? (please show all work)
For each of the following, give an example of a function g and a function f...
For each of the following, give an example of a function g and a function f that satisfy the stated conditions. Or state that such an example cannot exist. Be sure to clearly state the domain and codomain for each function. (a)The function g is a surjection, but the function fog is not a surjection. (b) The function g is not an injection, but the function fog is an injection. (c)The function g is an injection, but the function fog...
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.
Suppose that f is a bijection and f ∘ g is defined. Prove: (i). g is...
Suppose that f is a bijection and f ∘ g is defined. Prove: (i). g is an injection iff f ∘ g is; (ii). g is a surjection iff f ∘ g is.
Let A and B be nonempty sets. Prove that if f is an injection, then f(A...
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...
Let A and B be nonempty sets. Prove that if f is an injection, then f(A − B) = f(A) − f(B)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT