Relations and Functions
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16. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x {0, 1, 2, 3, 4, 5}}.
16. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x {0, 1, 2, 3, 4, 5}}.
16. Given, R = { (x, x+5): x {0,1,2,3,4,5}
= { (0,0+5), (1,1+5), (2,2+5), (3,3+5), (4,4+5), (5,5+5)}
= { (0,5), (1,6), (2,7), (3,8), (4,9), (5,10)}
So, domain of R= {0,1,2,3,4,5}
range of R= {5,6,7,8,9,10}
Upvote 
15. 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.
15. 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.
15. Given, A= {1,2,3,4,6}
R= { (a, b): a, b A, b is exactly divisible by a}
(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}
Upvote 14. The Fig 2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?
14. The Fig 2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?
14. As R is a relation from set P to Q.
(i) R = { (x, y): x – 2 = y ; 5 ≤ x ≤ 7}
(ii) R = { (5,3), (6,4), (7,5)}
Domain of R= {5,6,7}
range of R= {3,4,5}
Upvote 13. 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.
13. 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.
13. Given, A= {1,2,3,5}
B= {4,6,9}
R= { (x, y) : the difference of x & y is odd; x A, y B}.
= { (x, y):|x – y| is odd and x A, y B}
= { (1,4), (1,6), (2,9), (3,4), (3,6), (5,4), (5,6)}.
Upvote 12. 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.
12. 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.
12. Given, R = { (x, y): y = x + 5, x is a natural number less than 4; x, y N}
= { (x, y): y = x + 5; x, y N and x < 4}.
= { (1,1+5), (2,2+5), (3,3+5)}
= { (1,6), (2,7), (3,8)}
So, domain of R = {1,2,3}
range of R = {6,7,8}
Upvote Class 11 Math Chapter 2 Relation and Function Exercise 2.2
11. 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, co-domain and range.
Class 11 Math Chapter 2 Relation and Function Exercise 2.2
11. 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, co-domain and range.
11. Given, A = {1,2,3, …, 14}
R = { (x, y): 3x – y = 0; x, y A}
= { (x, y): 3x = y; x, y A}.
= { (1,3), (2,6), (3,9), (4,12)}
Domain of R is the set of all the first elements of the ordered pairs in R
So, domain of R= {1,2,3,4}
Codomain of R is the whole set A.
So, codomain of R= {1,
Upvote 10. 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.
10. 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.
10. Given, n (A × A)=9
n (A) ×n (A) = 9.
n (A)2 = 32.
n (A) = 3 .
And (–1,0), (0,1) A × A i.e., A × A = { (x, y), x A, y B}
? A= {–1,0,1}
And A × A= {–1,0,1} × {–1,0,1}
= { (–1, –1), ( –1,0), ( –1,1), (0, –1), (0,0), (0,1), (1, –1), (1,0), (1,1)}
Upvote 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.
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.
9. Given, n (A)=3
n (B)= 2
So, n (Ax B)=n (A).n (B)=3x 2=6
as (x, 1), (y, 2), (z, 1) ∈Ax B= { (x, y), x∈Aand y∈B}.
A= {x, y, z} and B= {1,2}
As n (A) = 3as n (B) = 2
Upvote 8. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
8. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
8. A Given, A= {1,2}
B= {3,4}
So, A× B= { (1,3), (1,4), (2,3), (2, 4)}
i.e., n (A ×B)=4
A ×B will have subset =24=16.They are,
Φ, { (1,3)}, { (1,4)}, { (2, 3)}, { (2,4)}, { (1,3), (1,4)}, { (1,3), (2,3)},
{ (1,3), (2, 4)}, { (1,4), (2, 3)}, { (1,4), (2, 4)}, { (2,3), (2, 4)},
{ (1,3), (1,4), (2,
Upvote