1. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Let R be the relation on ♬ defined by: For all f, gЄ F, fRg go f(1) = 2. (a) Is R reflexive, symmetric, antisymmetric, transitive? Prove your answers. (b) Is it true that for all functions ƒ Є F, there exists a function 9 € Ƒ so that fRg? Prove your answer. (c) Is it true that for all functions g = F, there exists a function f = Ƒ so that fRg? Prove your answer. (d) How many functions f = F are there so that fRf? Please simplify your answer to a number and provide your recipe.

Q: (d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest ne N such that x"…

A: By De Moivre's Theorem,  (cos x + isinx )n = cos nx + isin nx By Euler's formula eix= cos x + isin x

Q: Let A, B, C denote sets. Let g, h : A → B and f : B → C denote functions. Assume f is one-to-one and…

A:

Q: Let A={3,4,6,7}, and define a relation R on A as follows: For every x, y belong to A, xR y x|y.…

A: We first write elements of R then we form diagraph and then we write the corresponding adjacency…

Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and not…

A:

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: Let  X = {a, b, c}  and  Y = {d, e, f, g}.   Define functions H and K by the arrow diagrams below.…

A:

Q: 1. Let R be a relation on R x R such that (*1vi)Rs02) if and only if x,yı = x2y2. (a) Is (2,3)R(1,4)…

A: A relation from a set A to B is defined as a subset of A×B. Here R is a relation on ℝ×ℝ such that…

Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

A:

Q: Let A and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set…

A:

Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: Let A = {1, 2, 3, 4}. For any function f from A to A and any relation R on A, we define a relation S…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. Let R be the relation on the set A = (1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) e R if the…

A:

Q: Suppose that f : A → B is a function, viewed as a relation (set of ordered pairs). Let f* denote the…

A:

Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z x Y,…

A: Relation : A relation between two sets is a collection of ordered pairs containing one object from…

Q: IF A = { 1,1,2,3,5} B = {2,4} A relation S from A to B such that (x, y) ∈ S means that x ≤ 3 and y…

A:

Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: Which of the following is not true? I. All relations are functions. II. Bijection is a function that…

A:

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: a. Let A= {0,1,2,3} and define a relation R on A as follows: R= {(0, 2), (0, 3), (2, 0), (2, 1)}. i.…

A: Since you have posted multipart question and we can answer three subparts. So, answering the first…

Q: Part A: Suppose R is a relation defined on the set A = {1,2,3}. If R =…

A: Reflexive Property The Reflexive Property states that for every real number x , x=x . Symmetric…

Q: Question 5: Check whether the relation R in R defined as R = {[a, b): as b} is reflexive, symmetric…

A: Introduction :--

Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b – a)". So for example (6,2) € R and…

A:

Q: Let A = {d, e, f} and B = {0, 1} Define a relation as follows: ARB = {(d, 1), (f,0)} Select the…

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: QUESTION 2 Define a relation on Nx N as follows: (a, b) R (c,d) a+d=b+c (2.1) Is (3,6) R (3,5)?…

A: We have to show that the given relation is an equivalence relation.

Q: Given a relation g from the set D = {1, 2, 3, 4} to the set C = {a, b, c, d} where g= {(1, a), (2,…

A: A relation  from the set  to the set  where .The objective is to determine whether the relation is a…

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y ^ x, y = A} R"X =…

A: , and is a relation on .

Q: Suppose that R is a symmetric relation. Match the correct term with each blank space in the…

A: Suppose  that R is a symmetric relation than prove that R-1⊆R Proof: Suppose that &lt;x,y&gt;∈R-1.…

Q: Let E = {1, 2, 3} and F = {-2, –1, 0} and define a relation T from E to F as follows: For every (х,…

A: Since you have posted multipart question and we can answer three subparts. So, answering the first…

Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is (R = Reflexive, S = Symmetric, T =…

A: (a) Consider the Relation          V = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (2, 3), (3,…

Q: Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine…

A: Given:

Q: 1 Let A be the set of all integers = {...,-3,-2,-1,0,1,2,3,...}. Define the relation R on A as…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 2. Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9} and T = {2,4,6,8}. Let R be the relation on P (S), the power…

A: Kindly refer to Step 2 for the solution.

Q: etermine whether the relation defined below is reflexive, symmetric, and/or transitiv _swer. R is…

A: Given relationxRy on Z if x+y is even

Q: Define the following relations on A = {1,2,3,4}. Answer each of the following questions by listing…

A: