Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and justify whether R is reflexive, transitive, symmetric, and/or anti-symmetric.

Q: Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: Suppose A be any set and R is relation defined on A. Then R is transitive if whenever (a,b)∈R and…

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

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Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

A: Given  Set  = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b }   A…

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: Let R be a transitive relation on set A. Define Q to be {(r Prove or disprove that (RUR®)n (QU Qº)…

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Q: Consider the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b),…

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Q: let R be the relation on the set A = {1, 2, 3, 4, 5, 6} defined by a R bif and only if a = 2b.

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Q: let A be the relation on the set integers defined by s A t if and only if |a| <= |t|  is the…

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Q: 1. Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

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

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

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Q: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: Subject: Set Theory

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Q: Prove the understated statements concerning the relation &lt; on the set Z of all integers . If x…

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Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: We are given  that R is a transitive relation on a set A  Transitive Relation  A relation on a set X…

Q: 1. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: solution

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

A: Here given that the set is A = {a, b, c, d} and the relation on A is given by R = {(a, c), (b, b),…

Q: Suppose A is a set and R is a reflexive and transitive relation on A. Show that the

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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

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Q: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

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Q: Let S be the set of integers. If a, b E S, define aRb if ab &gt;= 0. Is R anequivalence relation on…

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Q: Let R be a total relation on a set of 15 elements. Then the number of ordered pairs in R is equal…

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: Let R be the relation on the set of integers such that a R b if and only if a = b or a = - b.…

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Q: Let A={1, 2, 5, 10}. Define the relation R on the base set A by: xRy if x/y is a whole number. Then…

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

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Q: Let R be the relation on the set of integers Z defined by m Rn iff m +n = 16. Determine whether R is…

A: Here, relation defined is, mRn iff m+n=16

Q: Let A={(m,n)∣m,n∈N and gcd(m,n)=1} and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc…

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Q: 18. Let X be a set. Define a relation R on P(X) by ARB AN B = ) for A, BE P(X). Determine whether…

A: We will use the definition of reflexivity, symmetry and transitivity to check the following :

Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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Q: Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of…

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Q: Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What…

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Q: 1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S,…

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Q: . Draw the Hasse diagram of the relation R on A, where A = (1, 2, 3, 4}, and R = {(1, 1), (1, 2),…

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Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) e a·d=b·c a - d…

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Q: etermine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Let A={(m,n)∣m,n∈N2 and gcd(m,n)=1}, and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc.…

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Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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Q: Define a relation on the set {a, b, c, d} that is (a) irreflexive and transitive, but not symmetric.…

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Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

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…