1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y that is onto, but not one-to-one. (b) Define a function g : X → Z that is one-to-one, but not onto. (c) Define a function h : X → X that is neither one-to-one nor onto.

Q: 3. Let f: A → B and g: B → C be functions. Recall that the composition of g and f is the function go…

A: a) To prove that if g and f are injective, then go f is injective, we need to show that for any two…

Q: (d) Given a function F : P({a, b, c}) → Z is defined by F(A) = |A| for all A E P({a,b, c}). i. Is Fa…

A: For the given function F(A)=|A| F will be one one if A=B implies F(A)=F(B) F will be onto if for a…

Q: Provide an example of a that is onto. Can this fun Justify your answer.

A:

Q: Show that if f is a meromorphic function on C such that C - ƒ(C) has at least three points then f is…

A: Here's how we can prove that if f is a meromorphic function on C such that C'-f(C) has at least…

Q: 5. Let f: Z → Z be defined by f(n) = n² + 1. (a). Is f a one-to-one function? Explain. (b). Is f an…

A: Given- The function is f(n)=n2+1 and f:ℤ→ℤ. Definition- Let a function from X to Y, One-to-one: If…

Q: Let F(R, R) be the set of all functions from R to R. For any f, g € F(R, R), we define fog € F(R, R)…

A: Given is set of all functions from set of reals to set of reals

Q: Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove…

A: We have to prove that g(x) = h(x) for all x belongs to B.

Q: Let D, E be non-empty sets, let ACD, let BCE, and let f: D E be a function. Prove that Anf¹(B) ≤…

A:

Q: Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o,…

A: X=o,p,s,wY=a,b,e,g,kZ=1,2,3,5,7,9f:X→Yf=o,a,p,g,s,e,w,bg:Y→Zg=g,3,e,2,b,9,k,7,a,1

Q: Let g : X c R"→ R be a function defined on the finite set X. Does g achieve a maximum and/or a…

A:

Q: (a) Define a function f: N→ N that is one-to-one but not onto. (b) Define a function f: N→ N that is…

A:

Q: Let f be a function, and suppose that A is a subset of the domain of f. The image of A under f is…

A: Let f be a function, and suppose that A is a subset of the domain of f. The image of A under f is…

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

A:

Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: 12. a. Suppose a function F: X→ Y is one-to-one but not onto. Is F-1 (the inverse relation for F) a…

A:

Q: Domain of F Co-domain of F X Y F a • d• Domain of G Co-domain of G X Y G a • b e of d• a. Is F…

A: