Advertisements
Advertisements
प्रश्न
Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by {(a, b) : a, b ∈ A, b is exactly divisible by a}
(i) Writer R in roster form
(ii) Find the domain of R
(ii) Find the range of R.
Advertisements
उत्तर
A = [1, 2, 3, 4, 5, 6]
R = {(a, b) : a, b ∈ A, b is exactly divisible by a}
(i) Here,
2 is divisible by 1 and 2.
3 is divisible by 1 and 3.
4 is divisible by 1 and 4.
5 is divisible by 1 and 5.
6 is divisible by 1, 2, 3 and 6.
∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), (6, 6)}
(ii) Domain (R) = {1, 2, 3, 4, 5, 6}
(iii) Range (R) = {1, 2, 3, 4, 5, 6}
APPEARS IN
संबंधित प्रश्न
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 = {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.
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}.
- Write R in roster form
- Find the domain of R
- Find the range of R.
Determine the domain and range of the relations:
(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and} \left| a \right| \leq 3 \right\}\]
Let A = {a, b}. List all relations on A and find their number.
For the relation R1 defined on R by the rule (a, b) ∈ R1 ⇔ 1 + ab > 0. Prove that: (a, b) ∈ R1 and (b , c) ∈ R1 ⇒ (a, c) ∈ R1 is not true for all a, b, c ∈ R.
If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(x, y) : x, y ∈ A × B and x > y}
If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.
If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =
A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is
If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y
Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs
Write the relation in the Roster Form. State its domain and range
R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`
Write the relation in the Roster Form. State its domain and range
R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}
Write the relation in the Roster Form. State its domain and range
R6 = {(a, b)/a ∈ N, a < 6 and b = 4}
Select the correct answer from given alternative.
The relation ">" in the set of N (Natural number) is
Answer the following:
If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range
R1 = {(1, 4), (1, 5), (1, 6)}
Answer the following:
If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range
R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
Answer the following:
R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is reflexive
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}
Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible
{(x, y) | y = x + 3, x, y are natural numbers < 10}
A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides ₹ 10,000, ₹ 25,000, ₹ 50,000, and ₹ 1,00,000 as salaries to the people who work in the categories A, C, M, and E respectively. If A1, A2, A3, A4, and A5 were Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3 were managers and E1, E2 was Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram
Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f : A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f
Discuss the following relation for reflexivity, symmetricity and transitivity:
The relation R defined on the set of all positive integers by “mRn if m divides n”
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”
Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it reflexive
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation
Choose the correct alternative:
Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is
If R1 = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R1.
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
Is the given relation a function? Give reasons for your answer.
t = {(x, 3) | x is a real number
Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.
Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.
