Why is the concept of function very important in mathematics ?

(a)  

Suppose A is a set of 2 colours and B is a set of 3 objects, i.e., A = {red, blue}and B = {b, c, s}, where b, c and s represent a particular bag, coat and shirt, respectively. How many pairs of coloured objects can be made from these two sets?

(a)  

Write the Definition 1

(a)  

If the three states, Delhi, Madhya Pradesh and Karnataka were making codes for the licence plates of vehicles, with the restriction that the code begins with an element from set A, which are the pairs available from these sets and how many such pairs will there be ?

(a)  

If (x + 1, y – 2) = (3,1), find the values of x and y

(a)  

If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

(a)  

Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find (i) A × (B ∩ C) (ii) (A × B) ∩ (A × C) (iii) A × (B ∪ C) (iv) (A × B) ∪ (A × C)

(a)  

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

(a)  

If R is the set of all real numbers, what do the cartesian products R × R and R × R × R represent?

(a)  

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

(a)  

question 👆

(a)  

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

(a)  

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

(a)  

State whether each of the following statements is 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

(a)  

If A = {–1, 1}, find A × A × A.

(a)  

If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

(a)  

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

(a)  

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

(a)  

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.

(a)  

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.

(a)  

Write Definition 2

(a)  

Write Definition 3

(a)  

Write Definition 4

(a)  

write the remarks

(a)  

Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x, y) : y = x + 1 } (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codomain and range of R.

(a)  

The Fig 2.6 shows a relation between the sets P and Q. Write this relation (i) in set-builder form, (ii) in roster form. What is its domain and range?

(a)  

Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.

(a)  

Write its remark.

(a)  

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

(a)  

Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

(a)  

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

(a)  

The figure shows a relationship between the sets P and Q. Write this relation

(i) in set-builder form (ii) in roster form

What is its domain and range?

(a)  

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

{(a, b): a, b ∈ A, b is exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R

(a)  

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}

(a)  

Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.

(a)  

Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

(a)  

Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.

(a)