Let X= (a, b, c) and as usual let X* denote the set of strings over X. Define a relation R on X by saying that aR3 if and only if a is a substring of 8. Explain why R is antisymmetric.

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

Q: Please help me with these questions. I am not understanding what I did wrong. Please kindly input…

A: With the given information. I found out that the number(How many they can marry) of each person can…

Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: Use a Green function to find the general solution of the differential equation y" + y = sec(t) - 2…

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Q: Define relation R on (Z+ U {0}) × Z+ by (a, b)R(c,d) if ad = bc. Describe the equivalence class [(2,…

A: Our objective is given below:

Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

Q: Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find…

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Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative f(t)=…

A: Original Functionf(t)=5t−3−5e0=5t3−5f(z)=ln100h(p)=−2e1−pFirst Derivative…

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: Let - be the relation on R\{0} given by x ~ y if and only if xy is positive. Prove that this is an…

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Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: Let A = {1, 2, 3}. Give an example of a relation R on A such that Ris symmetric but is not…

A: We have to give an example of a relation R on A such that R is symmetric but not anti-symmetric.A =…

Q: Let R be a reflexive relation on A. Show that R" is reflexive for all positive integers n.

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Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: Let R be a reflexive and transitive relation on A. Show that RN R¯' is an equivalence relation -1 on…

A: First let, A= set of integers. Then, let, R={(a,b):a,b in A} so,

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: Let R be the relation on the set of people with doctorates such that (a, b) ER if and only if a was…

A: Let A be the set of all people with doctorates and R be a relations on A defined by a,b∈R if and…

Q: Let R be a relation on A. Then for all n ≥ 0, prove R^n is a set. (Discrete Mathematics, powers of a…

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Q: Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A…

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Q: 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following:…

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Q: Suppose 1 and ₂ are equivalence relations on a set A. Let ~ be defined by the condition that a~ b if…

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Q: 8. (6 points) Define a relation R on Z as follows: For all integers m and n, m R n ⇒ (m − n)is a…

A: The objective of the question is to understand the properties of the relation R defined on the set…

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in…

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Q: . Define a relation R on Z as follows: a Rb if and only if 5 | (a²- 6²). Find four integers which…

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Q: Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈…

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Q: Let L be a relation on R such that for all x and y in R, x L y if and only if x < y. Give a counter…

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