Question

Let f : A → B, and let V ⊆ B. (a) Prove that V ⊇...

Let f : A → B, and let V ⊆ B.

(a) Prove that V ⊇ f(f−1(V )).

(b) Give an explicit example where the two sides are not equal.

(c) Prove that if f is onto then the two sides must be equal.

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
Consider Theorem 3.25: Theorem 3.25. Let f : A → B, let S, T ⊆ A,...
Consider Theorem 3.25: Theorem 3.25. Let f : A → B, let S, T ⊆ A, and let V , W ⊆ B. 1. f(S ∪T) = f(S)∪f(T) 2. f(S ∩T) ⊆ f(S)∩f(T) 3. f-1(V ∪W) = f-1(V )∪f−1(W) 4. f-1(V ∩W) = f-1(V )∩f−1(W) (a) Prove statement (2). (b) Give an explicit example where the two sides are not equal. (c) Prove that if f is one-to-one then the two sides must be equal.
Let f : A → B, g : B → C be such that g ◦...
Let f : A → B, g : B → C be such that g ◦ f is one-to-one (1 : 1). (a) Prove that f must also be one-to-one (1 : 1). (b) Consider the statement ‘g must also be one-to-one’. If it is true, prove it. If it is not, give a counter example.
1. a) Let f : C → D be a function. Prove that if C1 and...
1. a) Let f : C → D be a function. Prove that if C1 and C2 be two subsets of C, then f(C1ꓴC2) = f(C1) ꓴ f(C2). b) Let f : C → D be a function. Let C1 and C2 be subsets of C. Give an example of sets C, C1, C2 and D for which f(C ꓵ D) ≠ f(C1) ꓵ f(C2).
a)Suppose U is a nonempty subset of the vector space V over field F. Prove that...
a)Suppose U is a nonempty subset of the vector space V over field F. Prove that U is a subspace if and only if cv + w ∈ U for any c ∈ F and any v, w ∈ U b)Give an example to show that the union of two subspaces of V is not necessarily a subspace.
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
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
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.
Let g(u, v) = f(u 3 − v 3 , v3 − u 3 ). Prove...
Let g(u, v) = f(u 3 − v 3 , v3 − u 3 ). Prove that v^2 ∂g/∂u − u^2 ∂g/∂v = 0, using the Chain Rule
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 V denote the volume of a tetrahedron a, b, c the lengths of the three...
Let V denote the volume of a tetrahedron a, b, c the lengths of the three sides of one of its faces, and assume that each edge of the tetrahedron is equal in length to the opposite edge. Express V in terms of a, b, and c
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT