Page 22 - Mathematics Class - XI

Viva-Voce

1. What is meant by Cartesian product of sets?
Ans. In set theory, a Cartesian product is a mathematical operation that returns a set (or product set) from
multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b)
where a ∈ A and b ∈ B.
2. What is meant by an ordered pair?
Ans. An ordered pair consists of two objects or elements in a given fixed order.

3. If A = {1, 2} and B = {1, 2, 3}, then find A × B and n (A × B).
Ans. A × B = {1, 2} × {1, 2, 3}
= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}

n (A × B) = n (A) × n (B) = 2 × 3 = 6
4. If A = {a} and B = {b}, then find A × B and B × A. Is A × B = B × A?
Ans. A × B = {a} × {b} = {a, b}

B × A = {b} × {a} = {b, a}
Therefore, A × B ≠ B × A
5. Find the value of x and y if (x + 2y, y) = (3, x)

Ans. By the definition of ordered pair
x + 2y = 3 ...... (1) and y = x ...... (2)
Now putting the value of y from (2) into equation (1) So, y = x = 1

Then, x + 2x = 3 ⇒ 3x = 3 or x = 1 Then we can say that x = 1 and y = 1

MCQs

1. If (x + 2, y + 3) = (3, 5) then
a) x = –2, y = –3 b) x = 1, y = 2 c) x = 2, y = 1 d) x = –1, y = –2

2. If set A has 4 elements and set B has 3 elements then find the number of elements in A × B.
a) 12 b) 2 c) 16 d) 20
12
3. If A has 4 elements then A × A has elements

a) 4 b) 0 c) 1 d) 16
4. Which of the following ordered pair are equal
a) (p, q), (q, p) b) (4 × 1, 7 × 0), (4, 0) c) (12, 8), (8, 12) d) None of these

5. If A = {1, 2} and B = {1, 2, 3} then find the number of elements in A × B.
a) 6 b) 4 c) 3 d) 32

Answers: 1. b) x = 1, y = 2 2. a) 12 3. d) 16 4. b) (4 × 1, 7 × 0), (4, 0) 5. a) 6

20