5. Consider the permutations f 1 2 3 4 2 1 3 4 on the set {1, 2, 3, 4). (a) Find fog and go f. (b) F Find f, and verify that ƒoƒ-¹ = (c) ( Find g¹, and verify that and g= 1 2 3 4 3142 1 2 3 4 1 2 3 4 12 ) = 5¹ of 908¹-(1 2 3 4) = 9¹09 gog-¹ =g¹og

Q: Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1 Ą and fh = 1B. Prove…

A:

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

A:

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

A:

Q: 1. (10 points) Consider the set 2020n + 2021 S = :n = 1,2, 3, n+1 Find sup(S) and inf(S) and…

A: Since you have asked multiple questions, we will answer the first one. If you want other questions…

Q: Determine if 0 >=(61-6-J-RA) is in the span of = 0

A: Given: -1225 To check:If -1225 is in the span of Φ=1100, 1001, 0110, 0011 or not.

Q: ›) Prove that if the function ƒ is 1-1, then ƒ−¹ is a function. Caution! The ONLY assumptions here…

A: We use definition of function and one-one function to prove that f-1 is function.

Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x>24-2x2. It is required to prove the given expression for all…

Q: 1. The map T : Mat2,2(R) → Mat2,2(R) given by a +c d a b T c d а — d

A:

Q: Function f: {a,b)³ → (a,b) is defined by the following rule. For strings € (a,b)³, f(s) = f(x1x2x3)…

A:

Q: List whether each zero of g has even or odd multiplicity

A: To find the all x in R such that g(x) = 0  Since g(x) = 0 only at x = -1, 1, 3  (By graph it is easy…

Q: Let ƒ : Z → Z × Z be defined as f(n) = (2n, n + 3). Select which statements are true. a) for any in…

A:

Q: Show that the function f: [1, 2] → [1,8], f(x) = 7x - 6 is a bijection. What relationship exists…

A:

Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

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: The following functions all have domain {1, 2, 3, 4} and codomain {1, 2, 3, 4, 5}. For each,…

A: The domain of the given functions and the codomain .(a) (b) (c) The aim is to determine whether the…

Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: 1. This is one 1-1 correspondence between Z and I. f : I → Z f(n) = { n = 1, 3, 5, - …. 7, n = 2, 4,…

A: f(n)=n-12n=1,3,5,7,⋯-n2n=2,4,6,8,⋯

Q: 8) a) List the elements of each of the following sets, using the .' notation where necessary: i)…

A: Since it is multiple questions with multipart. As per our company guidelines, we have to solve the…

Q: 13. Let P(x) be the degree 10 polynomial through the 11 points (-5,5), (-4,5), (-3,5), (-2,5),…

A: We will find the value of P(6) using the Newton's forward difference interpolation polynomial of…

Q: 3. Iff and g are two lincar functions: f(x)-axtb and g(x)- cx+d, then what are the conditions on…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: CONSIDER A FUNCTION OF R IN R DEFINED BY: x² + 1 X-2 SO, THE EXPRESSION: f(x) - f(3) x - 3 FOR 2 IS…

A: f is a function of R in R defined by  f(x)=( x2+1)/(x-2)  Then expression [ f(x)-f(3)]/(x-3) ?

Q: 4. Define a relation R on N by aRb if a and b have no common factors except 1. (a) Give an example…

A: We have define  a relation R on natural numbers (N) by aRb if a and b have no common  factors except…

Q: K Match each function to its domain from the list below. Some domains may be used more than once,…

A:

Q: a. The remainder of P(x) = 2x' +mx? –7 when it is divided by x+2 is 6 greater than when it is…

A:

Q: 3. If f, g and h are functions so that the composition makes sense, then the composition of the…

A: Given :Associate property : h∘f∘g=h∘f∘g

Q: 13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all…

A: The objective of this question is to find the set of all even factors of given numbers using the…

Q: 6. (a) Let sets S = {A, B} × {1, 2, 3} and T = {A, B} × {1, 2, 3, 4} . How many different one %3| to…

A: The total number of elment in set s will be  and total number of element in set T will be

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

A:

Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

A:

Q: 3. Let A be a finite set. In this exertise functions f, g will be of type g: A →A and f: A → A. (a)…

A: Injective and surjective function

Q: 7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the…

A:

Q: 3. Assume f:{-3,0, 2, 11}{-11,0, 3, 5, 19} be a function given by f(-3) = 0, f(0) = -11,ƒ(2) =…

A:

Q: 2 3 4 5 6. f = 1 (i 43 5 2 6) (a) Write the permutation f' as a product of disjoint cycles,…

A: We can calculate the permutation of f7 from right to left then take the LCM of disjoint cycle

Q: Which of the following sets are countable? ORIN {7,99, 512}. 1 1 1 .}. " 10 100 1000 The set of all…

A: We know R is uncountable and N is coutable.  So, R \ N is uncountable [as R = (R \ N) U N, if R \N…