6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...

Question

Question

6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function with |XI, Yl< oo, i.e. X, Y ar

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

鵙,njective meong we wont have tuo Sol many-to-oneムNoTok As it is a fvnchon . so ane-to-many Jinot ok. But welan have qty, w Please let me know in comment section if I can help more on this problem.

Add a comment

Answer 2

Similar Homework Help Questions

Let X be a set with an equivalence relation ∼. Let f : X/ ∼→ Y...

Let X be a set with an equivalence relation ∼. Let f : X/ ∼→ Y be a function with domain as the quotient set X/ ∼ and codomain as some set Y . We define a function ˜f, called the lift of f, as follows: ˜f : X → Y, x 7→ f([x]). We define a function Φ : F(X/ ∼, Y ) → F(X, Y ), f 7→ ˜f. (1) Is Φ injective? Give a proof or a...
5. Let A = P(R). Define f : R → A by the formula f(x) =...

5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer
4. Let A be a non-empty set and f: A- A be a function. (a) Prove...

4. Let A be a non-empty set and f: A- A be a function. (a) Prove that f has a left inverse in FA if and only if f is injective (one-to-one) (b) Prove that, if f is injective but not surjective (which means that the set A is infinite), then f has at least two different left inverses.

1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers)...

1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers) and define function f: ℝ → {0,1}, where f(x) = XA(x) That is, f is the characteristic function of set A; it maps elements of the domain that are in set A (ie, those that are even integers) to 1 and all other elements of the domain to 0. By demonstrating a counter-example, show that the function f is not injective (not one-to-one). b)...
A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT...

A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT A1. Define g: C -> D by f(x)-g(x). Briefly, if g is not injective, then explain why f is not injective either. Let j : B → { 1, 2, 3, . . . , BI}...
How do I prove this function is not surjective? 3.) Let f: R-R, f(x)-x2+ x+1 and...

How do I prove this function is not surjective? 3.) Let f: R-R, f(x)-x2+ x+1 and Show that f is not injective and not surjective Justify that g is bijective and find gt. PIR, Show all the wortky) Not Surtechive: fx) RB Surjective: ye(o,oo) hng (g) 8 gon)-es is bijecelive g(x)-ex+s

Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explai...

Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explain why. (b) Determine if f is surjective. Explain why Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explain why. (b) Determine if f is surjective. Explain why
Let X and Y be any sets and let F be any one-to-one (injective) function from...

Let X and Y be any sets and let F be any one-to-one (injective) function from X to Y . Prove that for every subset A ⊂ X: (a) (10 points) A ⊂ F^(−1) (F(A)). (b) (10 points) F ^(−1) (F(A)) ⊂ A
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of...

Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of counting nuobors and the relation {(X Z〉 | Ye F and Z € Fand y-2). This relation is just a version of the usual subset relation, but restricted to only apply to the sets in F Prove: CFis a partial order. Prove: Cis not symmetric and connected. Prove: If R is an equivalence relation, it is also a euclidean...

Let h : X −→ Y be defined by h(x) :=    f(x) if...

Let h : X −→ Y be defined by h(x) :=    f(x) if x ∈ F g −1 (x) if x ∈ X − F Now we must prove that h is injective and bijective. Starting with injectivity, let x1, x2 ∈ X such that h(x1) = h(x2). Assume x1 ∈ F and x2 ∈ X −F. Then h(x1) = f(x1) ∈ f(F) and h(x2) = g −1 (x2) ∈ g −1 (X − F) = Y...

6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...

Homework Answers

Add Answer to:
6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...

Post as a guest

Earn Coins

Let X be a set with an equivalence relation ∼. Let f : X/ ∼→ Y...

5. Let A = P(R). Define f : R → A by the formula f(x) =...

4. Let A be a non-empty set and f: A- A be a function. (a) Prove...

1. a) Let A = {2n|n ∈ ℤ} (ie, A is the set of even numbers)...

A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT...

How do I prove this function is not surjective? 3.) Let f: R-R, f(x)-x2+ x+1 and...

Let f : R2-R2 be a function defin ed by f(x,y) (3+ z +y,) (a) Determine if f is injective. Explai...

Let X and Y be any sets and let F be any one-to-one (injective) function from...

Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of...

Let h : X −→ Y be defined by h(x) :=    f(x) if...

6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...

Homework Answers

Add Answer to: 6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...

Post as a guest

Earn Coins

Add Answer to:
6. Given a finite set A, denote IA] as a nurnber of elements in A. Let f : X → Y be a function wi...