Consider the subset relation C on the power set of {a,b,c}, that is P{a,b,c}. (a) Construct the table of predecessors and immediate predecessors of the relation.
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 B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…
A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}
Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…
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Q: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…
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Q: 8. Draw the directed graph of the binary relation S on B = { a, b, c, d, e} by S = {(a, b),(b,…
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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…
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Q: In the set A = {1,2, 3, 4} is defined a relation R by ? = {(1,1), (1,3), (3, 4), (4, 3)}. ndicate…
A: Given A = {1, 2, 3, 4} R = {(1, 1), (1, 3), (3, 4), (4, 3)}
Q: {(a, b) acb, a and b are finite set of integers}
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Q: Give a specific reason why the following set R does not define an equivalence relation on the set…
A: We will find out the required value.
Q: efine the relation ~ on the set N of positive integers by a~b if and only if a = b(10^k) for some…
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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…
A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…
Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P
A: Concept:
Q: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…
A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…
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 {2,3,4}{2,3,4} and {8,9,10}{8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and…
A: Given that: A={2,3,4}B={8,9,10}H is an relation from A to B such that: (x, y)∈H…
Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…
A: Solution:
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: 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: A particular relation * is defined on the set Z-{0} by x * y if and only if every prime factor of x…
A: Given that a particular relation is defined on the set ℤ-0 by…
Q: Let D be the relation on the natural numbers defined by the rule m divides n if and only if m does…
A: Let D be the relation on the natural number is defined by the rule m divides n if an only if m does…
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: 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: 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: 1. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…
A: solution
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: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…
A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.
Q: Suppose that P is a unary relation symbol, Q is a binary relation symbol, f is a unary function…
A: Note: According to bartleby we have to answer only first three subparts please upload the question…
Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…
A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…
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),…
A: Given R be the relation on the set S=1,2,3,a,b,c given by…
Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…
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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…
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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 X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…
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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: 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: . 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: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…
A: As per the condition, in every order pair there should be only 1 letter in common.
Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…
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Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…
A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…
Q: A relation * is defined on the set R-{0} by x * y if and only if xy > 0. For each of the following…
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Q: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…
A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…
Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…
A: Explanation of the answer is as follows
Q: Let Z be the set of integers and R be the relation on Z x Z defined by: Then R is (a,x)R(b, y) if…
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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: Determine whether the relation ? on the set of all people is reflexive, symmetric, antisymmetric,…
A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are…
Q: Consider the set A = {2, 3, 5, 7}. Create a relation R on A that is a partial order with at least…
A: The given set is A=2,3,5,7 and we have to define a partial order relation R on set A with at least…
Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an crder relation…
A: A partial order relation leads to poset which is very interesting.
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- In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.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.In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A. Determine in each case whether R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if xy. b. xRy if and only if xy.