PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N

Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:

(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N

Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).

If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x² + y² = 9, then write domain of R.

If R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4} is a relation defined on the set Z of integers, then write domain of R.

If R is a relation from set A = (11, 12, 13) to set B = (8, 10, 12) defined by y = x − 3, then write R⁻¹.

Let R = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b²) ∈ R, then write the values of a and b.

If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(x, y) : x, y ∈ A × B and x > y}

If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B

Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(x, y) : x − yis odd}. Write R in roster form. 

If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is

If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =

Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R⁻¹ is

If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is

If R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4} is a relation on Z, then the domain of R is ______.

A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is

A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?