[10 question added] Objective type question of Relation and Function

                                                
                                            


Question 1. >> If A = {-1 , 1, 3}, Then what is the number of relation of A ? 

Question 2. >> If A = {0,1,2,...,9} and the relation R on A is defined by R = {(x,y) : y ∊  A, y = 2x + 1} , then determine whether the relation R is -

1. Reflexive
2. Symmetric
3. Transitive

Question 3.>> If the relation R on set N of the natural no. is defined by R = {(a,b : a,b ∊ N , a = 2b - 1, b > 4 }. Is

1. (6 , 11 ) ∊ R
2. (13 , 7 ) ∊ R
3. (5 , 3 ) ∊ R

Question 4. >> If P be the set of people living in Delhi and R be the relation on P defined by 

R  = {(a , b) : a, b ∊ P, a lives within 4 km of b}. Determine whether R is transitive.

Question 5.>> Is the relation R on the set R of real number defined by R = {(a, b) : a, b ∊ R, 1 + ab > 0} transitive ? Justify your answer.

Question 6.>> Is the relation R on the set Q on the rational number defined by R = {(x, y) : x, y  ∊ Q, x < Y²

Question 7.>> If the relation R on the set A = {1, 2, 3} is defined by R ={(1, 1), (2, 2), (3, 3), (2, 1), (3, 2)} then determine whether the relation is -

1. Reflexive
2. Symmetric
3. Transitive

Question 8.>> If A = {1, 3, 7} and R on the set A = {1, 2, 3} is defined by R = {1,1}, Write R as a set of ordered pairs. Is this relation an equivalence relation ?

Question 9.>> The function ƒ : R --> R is defined by ƒ(x) = | 2x - 3 |

1. Is ƒ one-one
2. Is ƒ onto

Question 10.>> Find the range of the following functions : 

1. ƒ(x)=sin x+cos x
2. ƒ(x) = 3 sin x - 4 cos x.

SEE ANSWERS OF ALL THE ABOVE QUESTION