Advertisements
Advertisements
Question
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 reflexive
Solution
Given X = {a, b, c, d}
R = {(a, a), (b, b), (a, c)}
The minimum ordered pairs to be included to R in order to make R to be reflexive is (c, c) and (d, d)
APPEARS IN
RELATED QUESTIONS
The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`
The relation g is defined by g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`
Show that f is a function and g is not a function.
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
Let A = {a, b}. List all relations on A and find their number.
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.
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
If n(A) = 3, n(B) = 4, then write n(A × A × B).
If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x2 + y2 = 9, then write domain of 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.
If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is
Let R be a relation from a set A to a set B, then
Write the relation in the Roster Form. State its domain and range
R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`
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
R1 = {(1, 4), (1, 5), (1, 6)}
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:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
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
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R2 = {(–1, 1)}
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}
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”
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
Choose the correct alternative:
The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the following is true?
