Advertisements
Advertisements
प्रश्न
On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is transitive
उत्तर
N = the set of natural numbers.
R is the relation defined on N by
a R b if a + b ≤ 6
R = {(a, b), a, b ∈ N / a + b ≤ 6}
a + b ≤ 6 ⇒ b ≤ 6 – a
a = 1,
b ≤ 6 – 1 = 5
b is 1, 2, 3, 4, 5
∴ (1, 1), (1, 2), (1, 3), (1, 4), (1, 5) ∈ R
a = 2,
b ≤ 6 – 2 = 4
b is 1, 2, 3, 4
∴ (2, 1), (2, 2), (2, 3), (2, 4) ∈ R
a = 3,
b < 6 – 3 = 3
b is 1, 2, 3
∴ (3, 1), (3, 2), (3, 3) ∈ R
a = 4 ,
b < 6 – 4 = 2
b is 1, 2
∴ (4, 1), (4, 2) ∈ R
a = 5,
b < 6 – 5 = 1
b is 1
∴ (5, 1) ∈ R
∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}
Transitive:
(3, 1), (1, 5) ∈ R ⇒ (3, 5) ∉ R
∴ R is not transitive.
APPEARS IN
संबंधित प्रश्न
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 = [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.
Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R−1 is
If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is ______.
If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y
Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)
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
R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}
Select the correct answer from given alternative.
Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
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
Multiple Choice Question :
The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________
Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation
Choose the correct alternative:
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
Is the following relation a function? Justify your answer
R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`
If R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.
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 ______.
