Advertisements
Advertisements
Question
Let R be a relation on N defined by x + 2y = 8. The domain of R is
Options
(a) [2, 4, 8]
(b) [2, 4, 6, 8]
(c) [2, 4, 6]
(d) [1, 2, 3, 4]
Advertisements
Solution
(c) {2, 4, 6}
x + 2y = 8
⇒ x = 8 -2y
For y = 1, x = 6
y = 2, x = 4
y = 3, x = 2
Then R = {(2,3),(4,2),(6,1)}
∴ Domain of R = {2,4,6}
APPEARS IN
RELATED QUESTIONS
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 relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Find the inverse relation R−1 in each of the cases:
(ii) R = {(x, y), : x, y ∈ N, x + 2y = 8}
Find the inverse relation R−1 in each of the cases:
(iii) R is a relation from {11, 12, 13} to (8, 10, 12] defined by y = x − 3.
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.
Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.
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.
The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?
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 R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B
Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(x, y) : x − yis odd}. Write R in roster form.
R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is
If the set A has p elements, B has q elements, then the number of elements in A × B is
If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is
If R is a relation on a finite set having n elements, then the number of relations on A is
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
R4 = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}
Write the relation in the Roster Form. State its domain and range
R5 = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}
Write the relation in the Roster Form. State its domain and range
R7 = {(a, b)/a, b ∈ N, a + b = 6}
Identify which of if the following relations are reflexive, symmetric, and transitive.
| Relation | Reflexive | Symmetric | Transitive |
| R = {(a, b) : a, b ∈ Z, a – b is an integer} | |||
| R = {(a, b) : a, b ∈ N, a + b is even} | √ | √ | x |
| R = {(a, b) : a, b ∈ N, a divides b} | |||
| R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0} | |||
| R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls} | |||
| R = {(a, b) : Line a is perpendicular to line b in a plane} | |||
| R = {(a, b) : a, b ∈ R, a < b} | |||
| R = {(a, b) : a, b ∈ R, a ≤ b3} |
Select the correct answer from given alternative.
A relation between A and B is
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:
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, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R1 = {(2, 1), (7, 1)}
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the female 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
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 transitive
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
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?
Choose the correct alternative:
Let R be the universal relation on a set X with more than one element. Then R is
Is the following relation a function? Justify your answer
R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`
Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.
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.
Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.
