NCERT Book Class 11 Maths Relations And Functions Questions

2.1 Overview
This chapter deals with linking pair of elements from two sets and then introduce relations between the two elements in the pair. Practically in every day of our lives, we pair the members of two sets of numbers. For example, each hour of the day is paired with the local temperature reading by T.V. Station's weatherman, a teacher often pairs each set of score with the number of students receiving that score to see more clearly how well the class has understood the lesson. Finally, we shall learn about special relations called functions.

2.1.1 Cartesian products of sets
Definition : Given two non-empty sets A and B, the set of all ordered pairs (x, y), where x ∈ A and y ∈ B is called Cartesian product of A and B; symbolically, we write A × B = {(x, y) | x ∈ A and y ∈ B}
           If A = {1, 2, 3} and B = {4, 5}, then
              A × B = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)}
        and B × A = {(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}

(i) Two ordered pairs are equal, if and only if the corresponding first elements are equal and the second elements are also equal, i.e. (x, y) = (u, v) if and only if x = u, y = v.
(ii) If n(A) = p and n (B) = q, then n (A × B) = p × q.
(iii) A × A × A = {(a, b, c) : a, b, c ∈ A}. Here (a, b, c) is called an ordered triplet.
2.1.2 Relations A Relation R from a non-empty set A to a non empty set B is a

subset of the Cartesian product set A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.

The set of all first elements in a relation R, is called the domain of the relation R, and the set of all second elements called images, is called the range of R.

For example, the set R = {(1, 2), (– 2, 3), (1/2, 3)} is a relation; the domain o R = {1, – 2, 1/2 } and the range of R = {2, 3}.

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