State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric, and Transitive. Then construct three small worlds showing, respectively, that a relation can be Reflexive and not Symmetric, Symmetric and not Transitive, and Reflexive and not Transitive.

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

Q: R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than…

A: That's easy. Have a great day!!!

Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: Recall that, for any set A, the power set of A, P ( A ), is the set of all subsets of A. Consider…

A: To  find if the inclusion relation on P(A) has the properties of reflexivity, symmetry and…

Q: 1. Let A = {0,1,2,3,4,5}. Write out the relation R that expresses greater than orequal on A. Then…

A: Handwriting solution

Q: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² > 0 But, for n = 0…

Q: Suppose the following relations are defined on the set of A = {-2, -1,0 1, 2, }, . List the pairs in…

A: For relation R on a set A.   R is reflexive if (a,a)∈ R, for every a∈ A.   R is symmetric if (a,b)∈…

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: Let A = {a, b, c, d} where a, b, c, d are letters of the English alphabet. The following relations…

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Q: Does the relation "is a friend of" have a reflexive property (consider one person)? A symmetric…

A: Does the relation "is a friend of "  have a reflexive property (consider one person)?

Q: Let A be the set of students {Tom, Jim, Lisa, Mary}. Let B be the set of courses {C100, C200, C300}.…

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Q: For each of the following relations, determine whether it is (a) reflexive, (b) symmetric, (c)…

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Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

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Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

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Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

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Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: d) Let R be a relation on Z and x R y if x - y is even. e) Let R be a relation on N x N where (a, b)…

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Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Given R = {(m, m), (s, s), (e, e), (m, e), (s, e), (s, m), (e, m)} is a relation on set A = {m, e,…

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Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

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Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

A: (a) Let the set A=set of all watermelons in the truck and R be the relation on A, i.e R⊂A×A defined…

Q: Determine whether or not the following relations are equivalence relations on the given set. If the…

A: Let m, n, p∈ℚ Relation is m~n in ℚ if mn≥0 (i) Reflexive: Let m∈ℚ then mm=m2≥0 Therefore m~m   ∀m∈ℚ…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

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Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

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Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: Give an example of a relation which is a) One-one and onto b) Many - one and onto c) One-one and…

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Q: For each of the following, determine which of these choices is correct. Let Ry and Ry be two…

A: We have to determine which are correct.

Q: If an expoential relation such as y=bx, if b > 0 and b ≠ 1, then the y intercept is at zero. Is this…

A: The given problem is to check whether the y intercept is at zero is true or false.

Q: Determine the domain and range of each of the following relations. Use listing method for items 1…

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

Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

A: Prime numbers less than 10 are 2,3,5,7

Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

Q: The domain for a given relation is the set of all integers. Select the correct description of the…

A: we have given a relation that  x and y are related if and only if x and y are both negative or both…

Q: Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.

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Q: For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an…

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Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5} If the relation is…

A: To find: (i)the given relation is equivalence or not.             (ii) The equivalence class.

Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is…

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Q: The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of…

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