If f; N → N is a function defined by f = {(x, y): y = x 2 − 3x + 1}, find f −1 (5).
Answers
MATHEMATICS
CHAPTER: 2
RELATIONS AND FUNCTIONS
One mark questions
1. Define ordered pair.
If P and Q are two sets then pair of elements of P and Q written in small brackets and
grouped together in a particular order is defined as an ordered pair.
2. Find x , if (x + 1, 3 ) ≡ (2, 3)
( x+1, 3) ≡ (2, 3) => x + 1 =2
∴ x =1
3. Define Cartesian product of two sets.
Given two non-empty sets P and Q, the cartesian product PxQ is the set of all ordered
pair of elements from P and Q.
i.e.PxQ = {(p, q): p ∈ , ∈
}
4. If A = {a, b} and B = {1}, find A x B.
A X B = { (a, 1) , ( b, 1) }
5. If n (A) = p and n (B) = q, then find n (A x B).
Given n(A) = p and n(B) = q
∴ n (Ax B) = pq
6. If A = {1, 2, 3} and B is an empty set , then find A x B.
A xB = { }
7. Define on ordered triplet.
If P, Q and R are any three sets then the elements of P, Q and R written in small brackets
and grouped together in a particular order is defined as an ordered triplet.
8. If n (A) = 3 and A x A contains (a, b) and (b, c) , write A.
A = {a, b, c}
9. Define a relation R from the set A to the set B.
A relation R from a non-empty set A to a non – empty set B is a subset of the cartesian
product A xB