Consider the function f : {4, 6, 7, 8, 9} → {1, 2, 4, 5, 6, 9} given by the table below: 4 6 7 8 9 f(x) 1 2 5 96 X a. Is f injective? Why or why not? OYes, because every element in the codomain is the image of at most one element of the domain. No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain. b. Is f surjective? Why or why not? Yes, because every element in the codomain is the image of at most one element of the domain. O No, because at least one element in the codomain is the image of two or more elements of the domain. Yes, because every element in the codomain is the image of at least one element of the domain. O No, because at least one element in the codomain is not the image to an element of the domain.

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is an injective function…

A: We have to prove the given statement.

Q: Let A = {1, 3, 5, 6, 7, 9, 10, 12} and B = {1, 2, 3, 5, 7, 8, 9, 11, 12}. Consider the following…

A: Given a function f: A -> B , we have to determine whether it is injection, surjection,…

Q: Consider the function f : {1,2, 3, 4, 5} → {1,2,3, 4, 5} given by 2 3 4 5 f = 1 3 2 5 3 a. Find…

A:

Q: b) Let the set A = {-1,0, 1} and consider the following function: f2 A → A given by f₂(x) = (-x)4.…

A:

Q: ? ? ? ✓ 1. f = (1) v 3. f = 1 2 3 4 3) 55 55 x is even 2. f(x) = {(x+1)/2_if z is odd 1) 1 2 3 4 51…

A:

Q: 1 2 7 12 3 3 3 15 3 4 7 1 9

A: Recall that a relation f (also called correspondence or rule) from a set of objects A to another set…

Q: Theorem 13.6 Consider the function f:A – B. Let Uj and Uz be arbitrary subsets of the domain A, and…

A:

Q: Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are…

A:

Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: (a) Give an example of two functions f: A→B and g: B-C such that f is both 1-1 and onto but gof is…

A: (a)let's define sets 𝐴, 𝐵, and 𝐶 as follows:Let 𝐴={1,2}Let 𝐵={3,4}Let 𝐶={5}Now, let's define…

Q: Let f and g be defined by the following table:

A: We have the given table :       x  f(x) g(x) -2 6 0 -1 3 4 0 -1 1 1 -4 -3 2 0 -6…

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

A:

Q: Let A = {2, 3, 4, 5} and B = {6, 8, 10}. A relation R is defined from A to B by a R b if a | b and…

A:

Q: 24.4. Let A = {1, 2} and B = {3, 4). Write down all functions f : A → B. Indicate which are…

A: Given sets are    and                The cardinality of A is   (  Number of elements in A…

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let f : A → B and g : B C be surjective functions. Prove or disprove whether gof is surjective.

A: Here given that                       f :A→B   and    g :B→C  be both surjective function .  Now we…

Q: stinct parts.

A:

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Consider the set S = {x² + 1, 2x – 2, – x² + x}. The set S spans P2. If t(x) 2x? – 13x + 9 € P2 ,…

A: