Consider the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b), (a,c), (b,a), (b,c), (c,a), (c,b), (d,d), (f,f)}. Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Give reasons!

Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: 2) Let Q = {0,1,2,3} and define relation R on Q as follows: R = {(0,0), (0,1), (0,3), (1,0), (1,1),…

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Q: Let A be the set of all triangles defined by R = {(A1, A2) : A1 =A2). Show that R is an equivalence…

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Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and not…

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Q: ist the ordered pairs in the relation R from A = 0, 1,2, 3, 4, B = 1,2, 3, 4, 5, where Ris defined…

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Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: The relation R defined on a set A is antisymmetric if (a, b) ER = (b, a) E R for (A) Every (a, b) ER…

A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

Q: Exercise 1. Let R = {(x, y) | x, y E Z and x + y = 0, } be a relation on Z. Prove or disprove if R…

A: Let S be a non-empty set and R be a binary relation on S. (a) The relation R is said to be reflexive…

Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let R be the relation on N defined by R = {(n, m) EN x N: m=n+1). Then R is surjective. True False

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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

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

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y^x, y = A} R"X =…

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Q: Let A = {0, 1, 2, 3} and define relations R, S, and T on A as follows: %3D R = {(0, 0), (0, 1), (0,…

A: Let us first define the relations in this case, Reflexive : A set is reflexive if for a element in a…

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

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: A = Z*; a R b if and only if |a – b| < 2.

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Q: In the Cartesian plane = {(x, y): x,y E R} consisting of points with rectangular coordinates (x, y),…

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Q: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N₁ x + z = y}, where…

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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…

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: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

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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 X = {a, b, c}. Define a relation J on P(X) as follows: For all sets A and B in P(X), AJB A ANB #…

A: a) No  b) Yes  c) Yes

Q: B. Let A = (a, b. c. d). Let R be the relation on A defined as follows: R= {(a, a), (a, b), (a, c),…

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Q: 5. Let R be a relation on R2 defined by (w1,y1)R(x2y2) if and only if yı +x1 = y2 + x2. (a) Is R…

A: Given relation is

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

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Q: Consider the relation R = {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4}. Is R…

A: Definitions: Suppose R is relation defined on a set X then  i) R is reflexive if xRx, ∀x∈X. ii) R is…

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 A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (r, y)R(z, w)…

A: We will prove the given statement.

Q: Let A = {1, 2, 3, 4} and R be a relation defined on A. Given that R= {(1, 1), (1, 3), (2, 2), (2,…

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Q: Define a relation R on the x-y plane as follows: Given two points (x1 ,y1) and (x2 ,y2) in the x-y…

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Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

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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: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

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Q: Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive andtransitive but not…

A: Given, the relation R in R defined as R = {(a, b) : a ≤ b}.

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (2, w) in A, (r, y)R(z, w)…

A: Given that: A=Z+xZ+. Relation is:        For all (x, y) and (z, w) in A, (x, y)R(z, w)⇔x+w=z+y…

Q: Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}.…

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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: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: Let a relation R on R2 be given by (x,y)R(x’,y’) provided that x-x’ and y-y’ are integers. Prove…

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Q: Let R be the relation on the set A(1,2,3) defined by R-((1,1),(1,3),(3, 1).(3,3), then RORR…

A: It is given that R is the relation on the set A=1, 2, 3 such that  R=1, 1, 1, 3, 3, 1, 3, 3. We have…

Q: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3)} on the set A = {1,2,3,4,5}.…

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Q: Let R be a relation on Z. Then R is an equivalence relation if it is defined by xRy if and only if O…

A: A relation R between the elements of a set is said to be equivalence relation if it is: Reflexive…

Q: Let R be the relation on S = {a,b,c, d} given by the following digraph: b Then None of these R = (a,…

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Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (z, w) in A, (x, y)R(z,w) +…

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