Question

f(A − A0) = B −f(A0), if f is surjective, A0 ⊂ A.

f(A − A0) = B −f(A0), if f is surjective, A0 ⊂ A.

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
Prove that f : R → R where f(x) = |x| is neither injective nor surjective.
Prove that f : R → R where f(x) = |x| is neither injective nor surjective.
Let f : A → B and g : B → C. For each statement below...
Let f : A → B and g : B → C. For each statement below either prove it or construct f, g, A, B, C which show that the statement is false. (a) If g ◦ f is surjective, then g is surjective. (b) If g ◦ f is surjective, then f is surjective. (c) If g ◦ f is injective, then f and g are injective
Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective)....
Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective). (a)f:Z−→Z, f(n) =n2. (d)f:R−→R, f(x) = 3x+ 1. (e)f:Z−→Z, f(x) = 3x+ 1. (g)f:Z−→Zdefined byf(x) = x^2 if x is even and (x −1)/2 if x is odd.
Let f:A→B and g:B→C be maps. Prove that if g◦f is a bijection, then f is...
Let f:A→B and g:B→C be maps. Prove that if g◦f is a bijection, then f is injective and g is surjective.*You may not use, without proof, the result that if g◦f is surjective then g is surjective, and if g◦f is injective then f is injective. In fact, doing so would result in circular logic.
Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients...
Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients with an ? 0 ? a0 and there are relatively prime integers p, q ∈ Z with f ? p ? = 0, then p | a0 and q | an . [Hint: Clear denominators.]
Let G and H be groups and f:G--->H be a surjective homomorphism. Let J be a...
Let G and H be groups and f:G--->H be a surjective homomorphism. Let J be a subgroup of H and define f^-1(J) ={x is an element of G| f(x) is an element of J} a. Show ker(f)⊂f^-1(J) and ker(f) is a normal subgroup of f^-1(J) b. Let p: f^-1(J) --> J be defined by p(x) = f(x). Show p is a surjective homomorphism c. Show the set kef(f) and ker(p) are equal d. Show J is isomorphic to f^-1(J)/ker(f)
Part II True or false: a. A surjective function defined in a finite set X over...
Part II True or false: a. A surjective function defined in a finite set X over the same set X is also BIJECTIVE. b. All surjective functions are also injective functions c. The relation R = {(a, a), (e, e), (i, i), (o, o), (u, u)} is a function of V in V if V = {a, e, i, o, u}. d. The relation in which each student is assigned their age is a function. e. A bijective function defined...
Find the number N of surjective (onto) functions from a set A to a set B...
Find the number N of surjective (onto) functions from a set A to a set B where: (a) |A| = 8, |B| = 3; (b) |A| = 6, |B| = 4; (c) |A| = 5,|B| = 5; (d) |A| = 5, |B| = 7.
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f :...
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f : A → B using two-line notation. How many different functions are there, and why does this number make sense? (You might want to consider the multiplicative principle here). (b) How many of the functions are injective? How many are surjective? Identify these (circle/square the functions in your list). 3. Based on your work above, and what you know about the multiplicative principle, how many...
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f :...
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f : A → B using two-line notation. How many different functions are there, and why does this number make sense? (You might want to consider the multiplicative principle here). (b) How many of the functions are injective? How many are surjective? Identify these (circle/square the functions in your list). (c) Based on your work above, and what you know about the multiplicative principle, how many...