Relations: JEE Questions & Solutions

The number of relations, defined on the set {a, b, c, d}, which are both reflexive and symmetric, is equal to:

Let A = {2, 3, 5, 7, 9}. Let R be the relation on A defined by xRy if and only if 2x ≤ 3y. Let l be the number of elements in R, and m be…

Let the relation R on the set M = {1, 2, 3, …, 16} be given by R = {(x, y): 4y = 5x - 3, x, y ∈ M}. Then the minimum number of elements…

Let A = {-2, -1, 0, 1, 2, 3, 4}. Let R be a relation on A defined by xRy if and only if 2x + y ≤ 2. Let l be the number of elements in R.…

Let A = {0, 1, 2,..., 9}. Let R be a relation on A defined by (x, y) ∈ R if and only if |x - y| is a multiple of 3. Statement I: n(R) = 36.…

Let R be a relation defined on the set {1,2,3,4}×{1,2,3,4} by R={((a,b),(c,d)): 2a+3b=3c+4d} Then the number of elements in R is

The number of non-empty equivalence relations on the set {1,2,3} is:

Let A = {1,2,3}. The number of relations on A, containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is.

Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements needed to be added in R…

Let X = ℝ × ℝ. Define a relation R on X as: (a₁, b₁) R (a₂, b₂) ⇔ b₁ = b₂. Statement-I: R is an equivalence relation. Statement-II: For…

The relation R = {(x, y): x, y ∈ ℤ and x + y is even } is:

Define a relation R on the interval [ 0, π/2 ] by x R y if and only if sec² x - tan² y = 1. Then R is:

Let A be the set of all functions f: ℤ → ℤ and R be a relation on A such that R = { (f, g): f(0) = g(1) and f(1) = g(0) } Then R is:

Let A = {1, 2, 3, …, 100} and R be a relation on A such that R = {(a, b): a = 2b + 1}. Let (a₁, a₂), (a₂, a₃), (a₃, a₄), …, (a_k, a_(k+1))…

Let A = {-3,-2,-1,0,1,2,3}. Let R be a relation on A defined by xRy if and only if 0 ≤ x² + 2y ≤ 4. Let l be the number of elements in R…

Let A = {-2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by x R y if and only if y = max{x, 1}. Let l be the number of elements in R.…

Let A = {-3, -2, -1, 0, 1, 2, 3} and R be a relation on A defined by xRy if and only if 2x - y ∈ {0, 1}. Let l be the number of elements in…

The number of relations on the set A = {1, 2, 3} containing at most 6 elements including (1, 2), which are reflexive and transitive but not…

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements…

Let S = {1,2,3,…,10}. Suppose M is the set of all subsets of S, then the relation R = {(A,B): A∩ B ≠ ∅; A,B ∈ M} is:

Let R be a relation on ℤ × ℤ defined by (a, b)R(c, d) if and only if ad - bc is divisible by 5. Then R is:

If R is the smallest equivalence relation on the set {1, 2, 3, 4} such that {(1, 2), (1, 3)} ⊆ R, then the number of elements in R is:

The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is:

Let A = {1, 2, 3, 4} and R = {(1, 2), (2, 3), (1, 4)} be a relation on A. Let S be the equivalence relation on A such that R ⊂ S and the…

Let A = {1, 2, 3, 4, 5}. Let R be a relation on A defined by xRy if and only if 4x ≤ 5y. Let n be the number of elements in R and m be the…

The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an…

Let R be a relation defined on ℕ as a R b if 2a + 3b is a multiple of 5. Then R is:

The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric…

Let R be a relation on ℕ × ℕ defined by (a, b) R (c, d) if and only if ad(b - c) = bc(a - d). Then R is:

Among the relations S = { (a, b): a, b ∈ ℝ \ { 0 }, 2 + a/b > 0 } And T = { (a, b): a, b ∈ ℝ, a² - b² ∈ ℤ } which of the following is true?

Let R be a relation on ℝ, given by R = { (a, b): 3a - 3b + √7 is an irrational number } Then R is:

Let P(S) denote the power set of S = {1, 2, 3, …, 10}. Define the relations R₁ and R₂ on P(S) as A R₁ B if (A ∩ B^c) ∪ (B ∩ A^c) = ∅, and A…

Statement (P⇒ Q) ∧ (R⇒ Q) is logically equivalent to:

Let A = {1,2,3,4,…,10} and B = {0,1,2,3,4}. The number of elements in the relation R = {(a,b) ∈ A × A: 2(a-b)² + 3(a-b) ∈ B} is:

Among the statements: (S1): (p ⇒ q) ∨ ((¬ p) ∧ q) is a tautology (S2): (q ⇒ p) ⇒ ((¬ p) ∧ q) is a contradiction Choose the correct answer…

Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such that R = {(x, y) ∈ A × A: x - y is an odd positive integer or x -…

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B): a₁ divides b₂…

Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation defined on A × B such that R = {((a₁, b₁), (a₂, b₂)): a₁ ≤ b₂ and b₁…

The number of relations, on the set {1, 2, 3} containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is:

Let A = {-4, -3, -2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A: b = |a| or b² = a + 1} be a relation on A. Then the minimum number of elements…

Let A={1,2,3,4} and R be a relation on the set A× A defined by R={((a,b),(c,d)): 2a+3b=4c+5d} Then the number of elements in R is