On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th
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(c) Symmetric only• Let a ∈N. Then (a, a) ∉R as the GCD of ‘a’ and ‘a’ is ‘a’ not 2. R is not reflexive • Let a, b ∈N. Then, (a, b) ∉R ⇒ GCD of ‘a’ and ‘b’ is 2 ⇒ GCD of ‘b’ and ‘a’ is 2 ⇒ (b, a) ∈R ∴ R is symmetric • Let a, b, c ∈N. Then, (a, b) ∈R and (b, c) ∈ R ⇒ GCD of a and b is 2 and GCD of b and c is 2 \( ot\Rightarrow\) GCD of a and c is 2 R is not transitive For example, let a = 4, b = 10, c = 12 GCD of (4, 10) = 2 GCD of (10, 12) = 2 But GCD of (4, 12) = 4.
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Related questions

If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Description : If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

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Description : If R is a relation on a finite set A having n elements, then the number of relations on A is -Maths 9th

Last Answer : (d) \(2^{n^2}\)Set A has n elements ⇒ n(A) = n ⇒ A × A has n × n = n2 elements ∴ Number of relations on A = Number of subsets of A × A = \(2^{n^2}\)

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Description : Let R be a relation defined as a Rb if | a – b | > 0, then the relation is -Maths 9th

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Description : The relation ‘is less than’ on a set of natural numbers is -Maths 9th

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Description : For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th

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Description : Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then R is -Maths 9th

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Description : Which of the following is an equivalence relation defined on set A = {1, 2, 3} -Maths 9th

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A fuzzy set A on R is ................. iff A(λx1 + (1 – λ)x2) ≥ min [A(x1), A(x2)] for all x1, x2 ∈ R and all λ ∈ [0, 1], where min denotes the minimum operator. (A) Support (B) α-cut (C) Convex (D) Concave

Description : A fuzzy set A on R is ................. iff A(λx1 + (1 – λ)x2) ≥ min [A(x1), A(x2)] for all x1, x2 ∈ R and all λ ∈ [0, 1], where min denotes the minimum operator. (A) Support (B) α-cut (C) Convex (D) Concave 

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Description : Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on a set A = {1, 2, 3} is -Maths 9th

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Last Answer : (c) Reflexive and transitive onlyHere A = {3, 6, 9, 12} and R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 12), (3, 6)} ∵ (3, 3), (6, 6), (9, 9), (12, 12) all belong to R ⇒ {(a, a): ∈R V a ∈A} ... 12) ∈ R and (3,12) ∈ R ⇒ (3, 12) ∈ R (x, y) ∈ R, (y, z) ∈ R ⇒ (x, z) ∈ R Hence R is transitive.

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Last Answer : (d) 7A = {1, 2, 3}. R = {(1, 2), (2, 3)} To make R an equivalence relation, it should be: (i) Reflexive: So three more ordered pairs (1, 1), (2, 2), (3, 3) should be added to R to make it ... 2, 1), (3, 2), (1, 3), (3, 1)} is an equivalence relation. So minimum 7 ordered pairs are to be added.

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