Question

Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...

Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an example of a function f: A -> A with the indicated properties, or explain why no such function exists.

(a) f is bijective, but is not the identity function f(x) = x.

(b) f is neither one-to-one nor onto.

(c) f is one-to-one, but not onto.

(d) f is onto, but not one-to-one.

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
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T :...
1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X -> Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7} a) Explain why T is or is not a function. b) What is the domain of T? c) What is the range of T? d) Explain why T is or is not one-to one?
Let X = {1, 2, 3, 4} and Y = {2, 3, 4, 5}. Define f...
Let X = {1, 2, 3, 4} and Y = {2, 3, 4, 5}. Define f : X → Y by 1, 2, 3, 4 → 4, 2, 5, 3. Check that f is one to one and onto and find the inverse function f -1.
3 Let A = [0, 1) and B = (0, 1). Give an example to a...
3 Let A = [0, 1) and B = (0, 1). Give an example to a function f : A → B that is a) not one to one and not onto b) onto but not one to one c) one to one but not onto d*) one to one and onto
Discrete Math In this assignment, A, B and C represent sets, g is a function from...
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...
Remember that the DOMAIN is INTEGERS (....,-2,-1,0,1,2,3,4.......) and the TARGET is POSITIVE INTEGERS (1,2,3,4,.....) . Give...
Remember that the DOMAIN is INTEGERS (....,-2,-1,0,1,2,3,4.......) and the TARGET is POSITIVE INTEGERS (1,2,3,4,.....) . Give explanation and proofing for each . Find a function whose domain is the set of all integers and whose target is the set of all positive integers that satisfies each set of properties. (a) Neither one-to-one, nor onto. (b) One-to-one, but not onto. (c) Onto, but not one-to-one. (d) One-to-one and onto.
Let G = 〈(1 2 3 4 5 6), (1 6)(2 5)(3 4)〉. Let H1 :=...
Let G = 〈(1 2 3 4 5 6), (1 6)(2 5)(3 4)〉. Let H1 := 〈(1 4)(2 5)(3 6)〉 and H2 := 〈(1 6)(2 5)(3 4)〉. Determine if the subgroups H1 and H2 are normal subgroups of G.
Let f(x)=ln[x^3(x+5)^5(x^2+4)^6] f '(x)=
Let f(x)=ln[x^3(x+5)^5(x^2+4)^6] f '(x)=
For each problem below, either give an example of a function satisfying the give conditions, or...
For each problem below, either give an example of a function satisfying the give conditions, or explain why no such function exists. (a) An injective function f:{1,2,3,4,5}→{1,2,3,4} (b) A surjective function f:{1,2,3,4,5}→{1,2,3,4} (c) A bijection f:N→E, where E is the set of all positive even integers (d) A function f:N→E that is surjective but not injective (e) A function f:N→E that is injective but not surjective
If the first derivative function is f '(x) = (x −2) 4 ⋅(x −1) 3 it...
If the first derivative function is f '(x) = (x −2) 4 ⋅(x −1) 3 it follows that the parent function, f, has A. a relative minimum at x=1 only B. a relative maximum at x=1 C. both a relative minimum at x=1 and a relative maximum at x=2 D. neither a relative maximum nor a relative minimum E. None of the above
(6) (a) Give an example of a ring with 9 elements which is not a field....
(6) (a) Give an example of a ring with 9 elements which is not a field. Explain your answer. (b) Give an example of a field of 25 elements. Explain why. (c) Find a non-zero polynomial f(x) in Z3[x] such that f(a) = 0 for every a ? Z3. (d) Find the smallest ideal of Q that contains 3/4.