Скачать или смотреть CLASS 11|CHAPTER 2|Ex-2.1|INTRODUCTION|QUES- 1,2,3,4(I, II)|RELATION AND FUNCTION| BY VISHAL BHAIYA

CLASS 11|CHAPTER 2|Ex-2.1|INTRODUCTION|QUES- 1,2,3,4(I, II)|RELATION AND FUNCTION| BY VISHAL BHAIYA
#maths #ncert #class11maths #relationandfunction
 Ordered pair A pair of elements grouped together in a particular order.
 Cartesian product A × B of two sets A and B is given by
A × B = {(a, b): a ∈ A, b ∈ B}
In particular R × R = {(x, y): x, y ∈ R}
and R × R × R = {(x, y, z): x, y, z ∈ R}
 If (a, b) = (x, y), then a = x and b = y.
 If n(A) = p and n(B) = q, then n(A × B) = pq.
 A × φ = φ
 In general, A × B ≠ B × A.
 Relation A relation R from a set A to a set B is a subset of the cartesian
product A × B obtained by describing a relationship between the first element
x and the second element y of the ordered pairs in A × B.
 The image of an element x under a relation R is given by y, where (x, y) ∈ R,
 The domain of R is the set of all first elements of the ordered pairs in a
relation R.
 The range of the relation R is the set of all second elements of the ordered
pairs in a relation R.
 Function A function f from a set A to a set B is a specific type of relation for
which every element x of set A has one and only one image y in set B.
We write f: A→B, where f(x) = y.
 A is the domain and B is the codomain of f.
 The range of the function is the set of images.
 A real function has the set of real numbers or one of its subsets both as its
domain and as its range.
 Algebra of functions For functions f : X → R and g : X → R, we have
(f + g) (x) = f (x) + g(x), x ∈ X
(f – g) (x) = f (x) – g(x), x ∈ X
(f.g) (x) = f (x) .g (x), x ∈ X
(kf) (x) = k ( f (x) ), x ∈ X, where k is a real number.
( ) f x
g
      = ( )
( )
f x
g x , x ∈ X, g(x) ≠ 0
If
2 5 1 1
3 3 3 3
x
,y – ,
   
=        , find the values of x and y.
2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of
elements in (A×B).
3. If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
4. 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 ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.
5. If A = {–1, 1}, find A × A × A.
6. If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.
7. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
(i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.
8. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have?
List them.
9. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)
are in A × B, find A and B, where x, y and z are distinct elements.
The Cartesian product A × A has 9 elements among which are found (–1, 0) and
(0,1). Find the set A and the remaining elements of A × A.