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 equivalence
Advertisements
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)}
R is not an equivalence relation.
APPEARS IN
संबंधित प्रश्न
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
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 `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y
Write the relation in the Roster Form. State its domain and range
R5 = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}
Select the correct answer from given alternative
If A = {a, b, c} The total no. of distinct relations in A × A is
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 symmentric
Answer the following:
Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R3 = {(2, –1), (7, 7), (1, 3)}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}
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 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
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?
When are two ordered pairs \((a,b)\) and \((c,d)\) equal?
For a relation \(R\), the domain is the set of all:
Let \(A=\{1,2,3,4,5\}\), \(B=\{1,4,5\}\), and \((x,y)\in R\) imply \(x
Why is \(R=\{(1,4),(2,3),(3,2),(4,1)\}\) not a function on \(A=\{1,2,3,4,5\}\)?
