Question

Assume that X and Y are finite sets. Prove the following statement: If there is a...

Assume that X and Y are finite sets. Prove the following statement:
If there is a bijection f:X→Y then|X|=|Y|.
Hint: Show that if f : X → Y is a surjection then |X| ≥ |Y| and if f : X → Y is an injection then
|X| ≤ |Y |.

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
X，Y be sets and f:X-＞Y is a function there's a function g:Y-＞X such that g(f(x))＝x for...
X，Y be sets and f:X-＞Y is a function there's a function g:Y-＞X such that g(f(x))＝x for all x∈X Prove or disprove: f is a bijection   
.Unless otherwise noted, all sets in this module are finite. Prove the following statements! 1. There...
.Unless otherwise noted, all sets in this module are finite. Prove the following statements! 1. There is a bijection from the positive odd numbers to the integers divisible by 3. 2. There is an injection f : Q→N. 3. If f : N→R is a function, then it is not surjective.
Prove that if X and Y are disjoint countably infinite sets then X ∪ Y is...
Prove that if X and Y are disjoint countably infinite sets then X ∪ Y is countably infinity (can you please show the bijection from N->XUY clearly)
3. Prove or disprove the following statement: If A and B are finite sets, then |A...
3. Prove or disprove the following statement: If A and B are finite sets, then |A ∪ B| = |A| + |B|.
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...
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.
Please prove the following theorem: Suppose (X,p) and (Y,b) are metric spaces, X is compact, and...
Please prove the following theorem: Suppose (X,p) and (Y,b) are metric spaces, X is compact, and f:X→Y is continuous. Then f is uniformly continuous.
Is f(x) = x^3 - x an injection, surjection, or bijection? How do I know?
Is f(x) = x^3 - x an injection, surjection, or bijection? How do I know?
Let X and Y be sets. Prove X −(X −Y ) ⊆ X ∩Y . (Hint:...
Let X and Y be sets. Prove X −(X −Y ) ⊆ X ∩Y . (Hint: Remember that s ∈ S − T means s ∈ S and s ∈/ T . Thus, s ∈/ S − T means s ∈/ S or s ∈ T .)
Multiplicative Principle (in terms of sets): If X and Y are finite sets, then |X ×Y|...
Multiplicative Principle (in terms of sets): If X and Y are finite sets, then |X ×Y| = |X||Y|. D) You are going to give a careful proof of the multiplicative principle, as broken up into two steps: (i) Find a bijection φ : <mn> → <m> × <n> for any pair of natural numbers m and n. Note that you must describe explicitly a function and show it is a bijection. (ii) Give a careful proof of the multiplicative principle...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT