# CBSE Class 11 Maths Chapter 2: Relations and Functions (1 Mark Based Questions with Answers) Part-1

Q1: What is an ordered pair?

Answer: An ordered pair is a pair of entries in the specified order.

Q2: What is ordered 2-tuple?

Answer: Another name of an ordered pair.

Q3: If A and B are any two sets, write to represent an ordered pair of elements of A and B?

Answer: (a, b) : a ∈ A, b ∈ B

Q4: Is (a, b) = (b, a)?

Answer: No. a, b) ≠ (b, a) unless a = b

Q5: What is cartesian product of two sets A and B?

Answer: The set of all ordered pair of elements (a, b); a ∈ A, b ∈ B is called the cartesian product of two sets A and B and is denoted by A × B.

Symbolically,

A × B = {(a, b) : a ∈ A, b ∈ B}

Q6: When is A × B = ϕ?

Answer: When one or both of A, B are empty.

Q7: A = {1, 2, 3} and B = {4, 5}, then find

(I)  A × B

(II) B × A

(III) Are both equal?

(I) A × B = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)}

(II) B × A = {(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}

(III) No A × B ≠ B × A

Q8: If A × B = {(p, q), (p, r), (m, q), (m, r)}, find A and B.

Answer: A = Set of first elements = {p, m}

B = Set of second elements = {q, r}

Q9: What is an ordered triplet?

Answer: If A, B and C are three sets, then ordered triplet of elements means a triplet(a, b, c); a ∈ A, b ∈ B and c ∈ C in that order, is called an ordered triplet.

Q10: If A and B are two finite sets, then n(A × B) = ?

Answer:  n(A × B) = n(A) × n(B)

Q11: If the set A has 3 elements and the set B= {3, 4, 5}, then find the number of elements in (A × B).

Answer:  We haven n(A) = 3, n(B)= 3

Thus  n(A × B) = n(A). n(B)= 3 × 3 = 9

Hence, number of elements in A × B is 9.

Q12: If P {1, 2}, form the set P × P × P.

Answer: Given P = {1, 2}

∴ P × P × P = {(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)}

Q13: If A= {-1,1},find A × A × A.

Answer: We have, A = {-1, 1}

A × A × A= {(-1,-1,-1),(-1,-1,1),(-1,1,1),(1,-1,1),(1,1,-1),(1, -1,-1), (-1 , 1,-1), (1 , 1, 1)}.

Q14: State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.

(i) If P = {m,n} and Q = {n,m}, then P × Q ={(m,n),(n,m)}.

(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x,y) such that x ∈ B and y ∈ A.

(iii) If A = {1,2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.

(i) False.

Since, n(P) = 2, n(Q) = 2, therefore n(P × Q)=4.

Hence, P x Q= {(m, n), (m , m),(n, n ), (n, m)}.

Thus, the correct statement is:

If P= {m, n} and Q= {n, m}, then

P ×  Q = {(m, n), (m , m), (n , n), (n , m)}.

(ii) False.

The Correct statement is if A and B are non-empty sets, then A x B is nonempty

set of ordered pairs (x, y) such that x ∈ A and y ∈ B.

(iii) True.

Q15: Find x and y if:

(i) (4x+3,y) = (3x+5,–2)

(ii) (x–y,x+y)=(6,10)

(i) Since(4x+3,y)=(3x+5,–2),so 4x + 3 = 3x + 5

or x=2

and y=–2

(ii) x–y=6

x + y = 10

∴ 2x = 16 or x=8

8–y=6

∴ y=2