Find the domain and range of the relation

R = {(-1, 1), (1, 1), (-2, 4), (2, 4)}.

Let R = {(a, a³) : a is a prime number less than 5}.

Find the range of R.

Let R = {(a, a³) : a is a prime number less than 10}.

Find (i) R (ii) dom (R) (iii) range (R).

Let R = (x, y) : x + 2y = be are relation on N.

Write the range of R.

Let R ={(a, b): a, b ∈ N and a + 3b = 12}.

Find the domain and range of R.

Let R = {(a, b) : b = |a – 1|, a ∈ Z and la| < 3}.

Find the domain and range of R.

Let R = {(a, b) : a, b ∈ N and b = a + 5, a < 4}.

Find the domain and range of R.

Let S be the set of all sets and let R = {(A, B) : A ⊂ B)}, i.e., A is a proper subset of B. Show that R is (i) transitive (ii) not reflexive (iii) not symmetric.

Let A be the set of all points in a plane and let O be the origin. Show that the relation R = {(P, Q) : P, Q ∈ A and OP = OQ) is an equivalence relation.

On the set S of all real numbers, define a relation R = {(a, b) : a ≤ b}.

Show that R is (i) reflexive (ii) transitive (iii) not symmetric.

Let A = {1, 2, 3, 4, 5, 6) and let R = {(a, b) : a, b ∈ A and b = a + 1}.

Show that R is (i) not reflexive, (ii) not symmetric and (iii) not transitive.

Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.

Let A be the set of all triangles in a plane. Show that the relation

R = {(∆₁, ∆₂) : ∆₁ ~ ∆₂} is an equivalence relation on A.

Let R = {(a, b) : a, b ∈ Z and (a + b) is even}.

Show that R is an equivalence relation on Z.

Let R = {(a, b) : a, b ∈ Z and (a - b) is divisible by 5}.

Show that R is an equivalence relation on Z.

Show that the relation R defined on the set A = (1, 2, 3, 4, 5), given by

R = {(a, b) : |a – b| is even} is an equivalence relation.

Show that the relation R on N × N, defined by

(a, b) R (c, d) ⇔ a + d = b + c

is an equivalent relation.

Let S be the set of all real numbers and let

R = {(a, b) : a, b ∈ S and a = ± b}.

Show that R is an equivalence relation on S.

Let S be the set of all points in a plane and let R be a relation in S defined by R = {(A, B) : d(A, B) < 2 units}, where d(A, B) is the distance between the points A and B.

Show that R is reflexive and symmetric but not transitive.

Let S be the set of all real numbers. Show that the relation R = {(a, b) : a² + b² = 1} is symmetric but neither reflexive nor transitive.

Let R = {(a, b) : a = b²} for all a, b ∈ N.

Show that R satisfies none of reflexivity, symmetry and transitivity.

Show that the relation R = {(a, b) : a > b} on N is transitive but neither reflexive nor symmetric.

Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}.

Show that R is reflexive but neither symmetric nor transitive.

Let A = (1, 2, 3, 4) and R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (1, 3), (3, 2)}. Show that R is reflexive and transitive but not symmetric.

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Let A = {1, 2, 3} and let R = {(1, 1),
(2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}. Then, R is

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Let A = {a, b, c} and let R = {(a, a), (a, b), (b, a)}. Then, R is

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Let A = {1, 2, 3} and let R = {(1, 1),
(2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}. Then, R is

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Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b ⇔ a ⊥ b. Then, R is

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Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b ⇔ a || b. Then, R is

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Let Z be the set of all integers and let R be a relation on Z defined by a R b ⇔ (a - b) is divisible by 3. Then, R is

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Let R be a relation on the set N of all natural numbers, defined by a R b ⇔ a is a factor of b. Then, R is

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Let Z be the set of all integers and let R be a relation on Z defined by a R b ⇔ a≥ b. Then, R is

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Let S be the set of all real numbers and let R be a relation on S defined by a R b ⇔ |a| ≤ b. Then, R is

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Let S be the set of all real numbers and let R be a relation on S, defined by a R b ⇔ |a – b| ≤ 1. Then, R is

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Let S be the set of all real numbers and let R be a relation on S, defined by a R b ⇔ (1 + ab) > 0. Then, R is

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Let S be the set of all triangles in a plane and let R be a relation on S defined by ∆₁ S ∆₂⇔ ∆₁ ≡ A₂. Then, R is

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Let S be the set of all real numbers and let R be a relation on S defined by a R b ⇔ a² + b² = 1. Then, R is

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Let R be a relation on N × N, defined by
(a, b) R (c, d) ⇔ a + d = b + c. Then, R is

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Let A be the set of all points in a plane and let O be the origin. Let R = {(P, Q) : OP = QQ}. Then, R is

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Let Q be the set of all rational numbers, and * be the binary operation, defined by a * b = a + 2b, then

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Let a * b = a + ab for all a, b ∈ Q. Then,

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let Z be the set of all integers and let a * b = a – b + ab. Then, * is

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Let Z be the set of all integers. Then, the operation * on Z defined by

a * b = a + b - ab is

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Let Z⁺ be the set of all positive integers. Then, the operation * on Z⁺ defined by
a * b = a^b is

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Define * on Q - {-1} by a * b= a + b + ab. Then, * on Q – {-1} is