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: (d) How many functions f: A→ A are there so that fRIA? Explain.

A:

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A:

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A:

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A:

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A: Solution:

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

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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:

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A: Option A is correct.

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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…

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

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: 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:

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A: , and is a relation on .

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A: Given:

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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