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

Find the inverse relation R⁻¹ in each of the cases:

(ii) R = {(x, y), : x, y ∈ N, x + 2y = 8}

Find the inverse relation R⁻¹ in each of the cases:

Write the set of all vowels in the English alphabet which precede q.

Write the set of all positive integers whose cube is odd.

Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\]  in the set-builder form.

Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.

Determine the domain and range of the relation R defined by

(i) R = [(x, x + 5): x ∈ (0, 1, 2, 3, 4, 5)]

Determine the domain and range of the relation R defined by

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.