Give a specific reason why the following set R does not define an equivalence relation on the set {1,2 3,4}: {(1,1), (2,2), (3,3), (4,4), (2,3), (3,2), (2,4), (4,2)}
Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…
A: Given below the detailed solution
Q: Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an…
A: Equivalence classes: Let A be a nonempty set. Let R be the equivalence relation defined on A. Let…
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Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}
A: Set A={1,2,3,4,5,6}
Q: Prove that the relation of congruence is an equivalence relation.
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A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…
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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…
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Q: Let S be the equivalence relation on {− 1, 0, 1} × {0, 1, 2, 3} defined by (a, b )S(c, d) if and…
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Q: Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows: R = {(1, 1), (1, 2),…
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Q: Let B= {0,1,2,3,4} and let 0} , 1,3,4|,|2} be a partition of B that induces a relation Q. Find the…
A: Consider the given information.
Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…
A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4
Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…
A:
Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…
A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.
Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R? Note: Select the order that…
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Q: Let A = {1, 2, 3, 4, 5, 6} and R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 3), (3, 2)}.…
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Q: Given the relation R- {(1,1), (2.2). (3,3).(4.4), (1,2). (2,1). (3,4), (4,3)) on the set X…
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Q: Find the smallest relation containing the relation {(1, 2), (2, 3), (2, 4), (3, 1)} on the set {1,…
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Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…
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Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…
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Q: Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the…
A: Given: A={1, 2, 3, 4, 5, 6, 7} and R is the relation on this set defined s: (a, b)ϵR of the integer…
Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…
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Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…
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Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…
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Q: Let A={1,2,3,4,5,6} and let R be the equivalence relation on A defined by…
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Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…
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Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…
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Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…
A: Introduction :
Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…
A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…
Q: Which of these relations on {0, 1, 2, 3} are equivalence ?relations
A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…
Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…
A: We take counter example 9R10,10R11⇒9R 11
Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…
A: As per answering guideline, we can answer only one question at a time. Please repost other question…
Q: The number of equivalence relations on the set {1, 2, 3, 4} is
A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…
Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…
A: Consider the given information:
Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…
A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~ is defined by, "x1,x2~x3,x4 only if…
Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…
A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…
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: Find all equivalence relations on {1,2, 3}.
A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…
Q: Suppose R is a relation defined on the set A = {1, 2, 3}. If R = {(1,1), (1, 2), (2, 1), (2, 2), (3,…
A:
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Q: Suppose an equivalence relation R has the following equivalence classes that partition the set X.…
A: The ordered pairs in the equivalence relations produced by the given partitions {0, 2}, {1}, {3, 4}.…
Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…
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Q: Explain why consimilarity is an equivalence relation on M,.
A: Given that consimilarity is an equivalence relation on Mn.
Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…
A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…
Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…
A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,
Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :
A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4 Consider A=1,2,3,4
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- Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
- a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.