Q-3: a) Let R be a relation on A = {1,2,3,4} such that aRb means |ab| ≤ 1. Find the matrix representations for R² and R-1. b) Let R = {(1,2), (1,4), (2,3), (3,1), (4,2)} be a relation on {(1,2,3,4}. Find the symmetric and reflexive closures of R. c) Assume F is a relation on the set R of real numbers defined by xFy if and only if x - y is an integer. Prove that F is an equivalence relation on R.

Q: Identify the matrix that corresponds to the relation {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)).…

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Q: O (A) O (B) O (c) O (D) O (E) If the set {(1, 2, 1), (0, 1, 1), (1, -2, A)} is linearly independent,…

A: We have the set 1,2,1, 0,1,1, 1,-2, λ A set is linearly independent if the determinant of the matrix…

Q: Select one or more: transitive symmetric

A: Given, and Where be a relation on

Q: {0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine…

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Q: Let R be a relation on the set A = {0, 1, 4, 8} defined by xRy if and only if x + y < 8. (i) List…

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Q: . A) Write the ordered pairs, graphical representation, and the relation matrix, for  the Relation R…

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Q: 1. for  the Relation R ‘is a factor of’, on set A{1,2,3,6}. Write: A) the ordered pairs B) a…

A: Given the set A{1,2,3,6}

Q: Let R be the relation represented by the matrix M₂ [011] Γοιι 110 101 Identify the matrix that…

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Q: (i) Let A = {-1, 1,2,3,4}, X = {(-1, 1), (1, 1), (2, 2), (3, 3), (4, 4), (1, −1), (1, 4), (4, 1)}.…

A: We are allowed to do a maximum three sub parts as per bartleby guidelines

Q: Time left 1:18:. Let A = {0, 1, -1, 2} , R relation on A defined by R = {(a,b) : b= a², a, b e A}.…

A: We have check all such pairs of (a, b) lies on the given set or not?

Q: Suppose that A = {1, 2, 3} and B = {4, 6}. Let R be the relation from A to B containing (a, b) if a…

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Q: B2. (a) [2 Marks ] Show that the relation R in the set {1,2,3} given by R = {…

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Q: Let A = {2, 4, 5}, and let R be the relation on A consisting of pairs of the form (a, b), where ab…

A: Pairs in R is: {(4,4),(4,5),(5,4),(5,5)} Only these have ab&gt;12

Q: Let A = {1, 2, 3, 4, 5, 6}, and consider the following equivalence relation on A: R = {(1, 1),  (2,…

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Q: Let A = {1, 2, 3, 4}. Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4, 3)}…

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Q: V = Span{(1, 2, 3), (1, 0, 2)} and W = Span {(0, 2, 1), (1, 1, 1)}. Find the relation between V and…

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Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: A, BE RXn Let n EN. Consider the following binary relation for A~B 3Qe R"*" : Q. A A = QB orthogonal…

A: We will be solving part (b) as mentioned. Let n∈ℕ. Consider the given binary relation for A,B∈ℝn×n…

Q: (3) Let S be the equivalence relation on {0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

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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: Let R be the relation on the set A = {a1, a2, a3, a4} whose matrix is given by 1 0 1 0 0 1 0 1 1 0 1…

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Q: There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (1) {(0,…

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Q: Let 4= {1, 2, 3, 4, 5, 6} and the relation R on A is defined by R = {(a,b)|a + b is prime; a, b E A}…

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Q: A// Which of these relations on {0, 1 , 2, 3 } are equivalence relations, why? a) R1= {(0, 0). (1 ,…

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: Q3) Consider the relation R = {(1,3), (1,4), (3, 2), (3, 3), (3, 4)} on A = {1,2, 3, 4} a) Find the…

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Q: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

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Q: Let A = {1, 2, 3, 4). Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4,3)}…

A: Since you have posted a multi subparts question according to guidelines I will solve first…

Q: 1. Given A = {1, 2, 3, 4}, B = {a, ß,7} and R= {(2,B), (2, 7), (4, B), (1, a), (1, 7)} (a) Determine…

A: Here given that                        A={1, 2, 3, 4}                        B={α, β, γ}      And…

Q: A.  Write the relation on {a, b, c, d} in matrix form. 1.  {(a, a), (a, d), (b, c), (c, d), (d, a),…

A: The matrix form of a relation is given by M=Mij , where Mij=1    if ai,bj∈R0    if ai,bj∉R Part(1)…

Q: a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the…

A: let A={1,2,3,4}   aRb iff 2a&gt;b+1   first we will find R…