Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Ex 3(a) Textbook Exercise Questions and Answers.

## CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Exercise 3(a)

Question 1.

Compute the product A × B when

(i) A = {0} = B

(ii) A = {a, b}, B = {a, b, c}

(iii) A = Z, B = Φ

Solution:

(i) A = {0} = B

∴ A × B = {(0, 0)}

(ii) A = {a, b}, B = {a, b, c}

∴ A × B = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c)}

(iii) A = Z, B = Φ ∴ AxB = Φ

Question 2.

If |A| = m, |B| = n, what can you say about

(i) |A × B| (ii) |P(A) × P(B)|

Solution:

If |A| = m. |B| = n then

(i) lA × B| = mn.

(ii) |P(A)| = 2^{m} . |P(B)| = 2^{n}

∴ |P(A) × P(B)| =2^{m} × 2^{n} = 2^{m+n}

Question 3.

Find x, y if

(i) (x, y) = (-3, 2)

(ii) {x + y, 1) = (1, x – y)

(iii) (2x + y, 1) = (x, 2x + 3y)

Solution:

(i) ∴ x = – 3, y = 2

(ii) ∴ x + y = 1, x – y = 1

∴ 2x = 2 or, x = 1

∴ y=0

(iii) ∴ 2x + y = x, 1 = 2x + 3y

∴ {x + y = 0} × 2

2x + 3y = 1

– – –

∴ – y = – 1 or, y = 1

∴ x = – 1

Question 4.

If, A × B = B × A then what can you

Solution:

If A × B = B × A then A = B

Question 5.

|A × B| = 6. If ( -1, y ), (1, x), (0, y) are in A × B. Write other elements in A × B, where x ≠ y.

Solution:

Let |A × B| = 6 and (-1, y) (1, .x) (0, y) ∈ A × B

⇒ -1, 1, 0 ∈ A and x, y ∈ B

As |A × B| = 6 and 3 × 2 = 6

We have A = {-1, 1, 0} and B = {x, y}

Thus other elements of A × B is (-1, x) , (1, y), (0, x)