Advertisements
Advertisements
Question
Write the relation in the Roster Form. State its domain and range
R6 = {(a, b)/a ∈ N, a < 6 and b = 4}
Advertisements
Solution
Let R6 = {(a, b)/a ∈ N, a < 6 and b = 4}
= {(1, 4), (2, 4), (3, 4), (4, 4), (5, 4)}
Domain of R6 = set of first elements of ordered pairs of R6
={1, 2, 3, 4, 5}
Range of R6 = set of second elements of ordered pairs of R6
= {4}
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.
Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.
Determine the domain and range of the relation R defined by
(i) R = [(x, x + 5): x ∈ (0, 1, 2, 3, 4, 5)]
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.
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?
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
(iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ∈ N × N
If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).
Let R = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.
If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =
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 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
Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs
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
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.
The relation ">" in the set of N (Natural number) 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 reflexive
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.
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R2 = {(–1, 1)}
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
Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible
{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}
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}
Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f : A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”
Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it symmetric
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
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:
Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is
Choose the correct alternative:
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
Choose the correct alternative:
Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is
Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.
Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.
A relation on the set A = {x : |x| < 3, x ∈ Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x| ≠ –1}. Then the number of elements in the power set of R is ______.
