Class 11 Mathematics | NCERT Exercise 2.2 | Solved Answers and Questions #eduvictors #class11Maths

 Class 11 Maths | NCERT Exercise 2.2 | Solved Answers and Questions

CHAPTER: RELATIONS AND FUNCTIONS

Q1. 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.

Answer: Here y = 3x

R from A×A= {(1,3), (2,6), (3,9), (4,12)}

The domain of R is the set of all first elements of the ordered pairs in the relation.

Domain ={1,2,3,4}

Codomain = {1,2,3,...,14}

Range = {3,6,9,12}

Q2. 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.

Answer: R = {(1,6), (2,7), (3, 8)}

Domain = {1,2,3}

Range = {6,7,8}

Q3. 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.

Answer: R = {(1,4), (1,6), (2,9), (3, 4), (3,6), (5,4), (5,6)}

Q4. Figure 2.7 shows a relationship between the sets P and Q. Write this relation

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

Answer: P = {5,6,7} and Q = {3,4,5}

R = {(x,y): y = x-2; x∈P} OR R = {(x, y) : y = x – 2 for x = 5, 6, 7}

R = {{5,3), (6,4), (7,5)}

Domain of R = {5, 6, 7}, Range of R = {3, 4, 5}

Q5. 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

Answer:

(i) R = {(1,1), (1,2), (1,3), (1,4) (1,6), (2,2) (2,4), (2,6), (3,3) (3,6), (4,4), (6,6)}

(ii) Domain of R = {1,2,3,4,6}

(iii) Range of R = {1,2,3,4,6}

Q6. Determine the domain and range of the relation R defined by

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.

Answer: relation = {(0,5), (1,6), (2,7), (3,8), (4,9), (5,10)}

Domain = {0,1,2,3,4,5}

Range = {5,6,7,8,9,10}

Q7. Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.

Answer: Relation R = {(2,8), (3,27), (5, 125), (7, 343)}

Q8. Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

Answer: n(A) = 3 and n(B) = 2

 A × B = {(x, 1), (x, 2), (y, 1), (y, 2), (z, 1), (z, 2)}

 Thus n(A × B) = 2×3 = 6

 Thus the number of relations from A to B = 2⁶ = 64

Note: The total number of relations that can be defined from a set A to a set B is the number of possible subsets of A × B. If n(A ) = p and n(B) = q, then n (A × B) = pq and the total number of relations is 2^pq.

Q9. 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.

Answer: R = {(a, b): a, b ∈ Z, a – b is an integer}

It is known that the difference between any two integers is always an integer.

∴ The domain of R = Z (all integers)

  Range of R = Z (all integers)

👉SEE ALSO:

Ch2: Relations and Functions (1 Mark Q & A) Part-1
Ch2: Cartesian Product of Two Sets (Important Points)
Ch2: Relations - Domain, Range and Co-Domain (Solved Problems)
Ch2: NCERT Exercise 2.1 (Solved)