PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Determine the domain and range of the relations:

(i) R = {(a, b) : a ∈ N, a < 5, b = 4}

Determine the domain and range of the relations:

(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and}  \left| a \right| \leq 3 \right\}\]

Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b²}. Is the statement true?

(a, b) ∈ R implies (b, a) ∈ R

Justify your answer in case.

Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b²}. Is the statement true?

(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

Justify your answer in case.

Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(x, y) : 3x − y = 0, where x, y ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.

Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by {(a, b) : a, b ∈ A, b is exactly divisible by a}

(i) Writer R in roster form
(ii) Find the domain of R
(ii) Find the range of R. 

The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?

For the relation R₁ defined on R by the rule (a, b) ∈ R₁ ⇔ 1 + ab > 0. Prove that: (a, b) ∈ R₁ and (b , c) ∈ R₁ ⇒ (a, c) ∈ R₁ is not true for all a, b, c ∈ R.

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.