Advertisements
Advertisements
Question
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
Advertisements
Solution
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)}.
R is not reflexive since (a, a) ∉ R for all a ∈ N.
APPEARS IN
RELATED QUESTIONS
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 R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?
(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R
Justify your answer in case.
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.
If R is a relation on a finite set having n elements, then the number of relations on A is
If (x − 1, y + 4) = (1, 2) find the values of 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
R6 = {(a, b)/a ∈ N, a < 6 and b = 4}
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:
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
R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}
Answer the following:
Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}
A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range
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?
Is the following relation a function? Justify your answer
R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`
If R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.
Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.
Which statement defines a relation from set \(A\) to set \(B\)?
Which statement violates the condition for a function?
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?
