Advertisements
Advertisements
प्रश्न
On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is transitive
Advertisements
उत्तर
Given N = set of natural numbers
R is the relation defined by a R b if 2a + 3b = 30
3b = 30 – 2a ⇒ b = `(30 - 2a)/3` a, b ∈ N
a = 1, b = `(30 - 2)/3 = 28/3 ∉ "N"`
a = 2, b = `(30 - 4)/3 = 26/3 ∉ "N"`
a = 3, b = `(30 - 6)/3 = 24/3` = 8 ∈ N
∴ (3, 8) ∈ R
a = 4, b = `(30 - 8)/3 = 22/3 ∉ "N"`
a = 5, b = `(30 - 10)/3 = 20/3 ∉ "N"`
a = 6, b = `(30 - 12)/3 = 18/3` = 6 ∈ N
∴ (6, 6) ∈ R
a = 7, b = `(30 - 14)/3 = 16/3 ∉ "N"`
a = 8, b = `(30 - 16)/3 = 14/3 ∉ "N"`
a = 9, b = `(30 - 18)/3 = 12/3` = 4 ∈ N
∴ (9, 4) ∈ R
a = 10, b = `(30 - 20)/3 = 10/3 ∉ "N"`
a = 11, b = `(30 - 22)/3 = 8/3 ∉ "N"`
a = 12, b = `(30 - 24)/3 = 6/3` = 2 ∈ N
∴ (12, 2) ∈ R
a = 13, b = `(30 - 26)/3 = 4/3 ∉ "N"`
a = 14, b = `(30 - 28)/3 = 2/3 ∉ "N"`
a = 15, b = `(30 - 30)/3 = 0/3` = 0 ∈ N
When a > 15, b negative and does not belong to N.
∴ R = {(3, 8), (6, 6), (9, 4), (12, 2)}.
Clearly R is transitive since we cannot find elements (a, b), (b, c) in R such that (a, c) ∉ R
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.
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N
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
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P
Select the correct answer from given alternative.
A relation between A and B is
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
Answer the following:
Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}
Answer the following:
Show that the following is an equivalence relation
R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}
Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R
On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is reflexive
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
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
Choose the correct alternative:
Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?
Choose the correct alternative:
The number of relations on a set containing 3 elements is
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
The Cartesian product \(A\times A\) has \(9\) elements and contains \((-1,0)\) and \((0,1)\). What is \(A\)?
For \(R=\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)\}\) from \(A\) to \(B=\{1,4,5\}\), which statement is correct?
