If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? Give reasons in support of your answer. (i) {(1, 6), (3, 4), (5, 2)} (ii) {(1, 5), (2, 6), (3, 4), (3, 6)} (iii) {(4, 2), (4, 3), (5, 1)} (iv) A×B Watch Solution
A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows (x, y)∈R ⟺ x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range. Watch Solution
let A be the set of first five natural numbers and let R be a relation on A defined as follow: (x, y)∈R ⟺ x ≤ y. Express R and R^-1 as sets of ordered pairs. Determine also (i) the domain of R^-1 (ii) the range of R. Watch Solution
Find the inverse relation R^-1 in each of the following case : R = {(1,2),(1,3),(2,3),(3,2),(5,6)} Watch Solution
Find the inverse relation R^-1 in each of the following case : R = {(x, y) : x, y ∈ N, x + 2 = 8} Watch Solution
Find the inverse relation R^-1 in each of the following case : R is a relation form.{11, 12, 13} to {8, 10, 12} defined by y = x – 3 Watch Solution
Write the following relation as the sets of ordered pairs : A relation R from the set {2, 3, 4, 5, 6} to the set {1,2,3} defined by x = 2y. Watch Solution
Write the following relation as the sets of ordered pairs : A relation R on the set {1, 2, 3, 4, 5, 6, 7} defined by (x, y)∈R ⟺ x is relatively prime to y Watch Solution
Write the following relation as the sets of ordered pairs : A relation R on the set {0, 1, 2…,10} defined by 2x + 3y = 12. Watch Solution
Write the following relation as the sets of ordered pairs : A relation R from a set A = {5, 6, 7, 8} to the set B = {10,12,15,16,18} defined by (x, y)∈R ⟺ x divides y. Watch Solution
Let R be relation in N defined by (x, y)∈ R ⟺ x + 2y = 8. Express R and R^-1 as sets of ordered pairs. Watch Solution
Let A = {3, 5} and B = {7, 11}. Let R = {(a, b): a∈A, b∈B, a – b is odd}. Show that R is an empty relation from A into B. Watch Solution
Let A = {1, 2} and B = {3, 4}. Find the total number of relations from A into B. Watch Solution
Determine the domain and range of the following relation : R = {(x, x+5) : x ∈ {0, 1, 2, 3, 4, 5}} Watch Solution
Determine the domain and range of the following relation : R = {(x, x^3) : x is a prime number less than 10} Watch Solution
Determine the domain and range of the following relation : R = {(a, b) : a ∈ N, a less than 5, b = 4} Watch Solution
Determine the domain and range of the following relation : S = {(a, b) : b= |a – 1|, a ∈ Z and |a| ≤ 3} Watch Solution
Let A = {a, b}. List all relations on A and find their numbers. Watch Solution
Let A = {x, y, z} and B = {a, b}. Find the total number of relations from A into B. Watch Solution
Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b^2}. Are the following statements true? (i) (a, a)∈R for all a∈N (ii) (a, b)∈R ⇒ (b, a)∈R (iii) (a, b)∈ R and (b, c) ∈ ⇒ R (a, c) ∈R Watch Solution
Let A = {1, 2, 3….,14}. Define a relation on a set A by R = {(x, y) : 3x – y = 0, where x, y∈ A}. Depict this relationship using an arrow diagram. Write down its domain, co-domain and range. Watch Solution
Define a relation R on the set N of natural number by R = {x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range of R. Watch Solution
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. Watch Solution
Write the relation R = {(x, x^3) : x is a prime number less than 10} in roster form. Watch Solution
Let A = {1,2,3,4,5,6}. Let R be a relation on A defined by R = {(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 Watch Solution
Figure 2.15 shows a relationship between the set P and Q. Write the relation in (i) set builder form. (ii) roster form. What is its domain and range? Watch Solution
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. Watch Solution
For the relation R1 defined on R by the rule (a, b)∈R1 ⟺ 1 + ab greater than 0. Prove that: (a, b) ∈ R1 and (b, c) ∈ R1 ⇒ (a, c)∈R1 is not true for all a, b, c ∈ R. Watch Solution
let R be a relation on N×N defined by (a, b)R(c, d)⟺a + b = b + c for all (a, b),(c, d)∈ N×N Show that : (i) (a, b)R(a, b) for all (a, b) ∈N×N (ii) (a, b)R(c, d)⇒(c, d)R(a, b) for all (a, b),(c, d)∈ N×N (iii) (a, b)R(c, d) and (c, d)R(e, f) ⇒(a, b)R(e, f) for all (a, b),(c, d),(e, f)∈ N×N Watch Solution
Chapter 2: Relations – R. D. Sharma Class 11th Maths