Advertisements
Advertisements
प्रश्न
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}
Advertisements
उत्तर
a. Since, a = a
∴ (a, a) ∈ R
∴ R is reflexive.
b. Let (a, b) ∈ R
Then a = b
∴ b = a
∴ (b, a) ∈ R
∴ R is symmetric.
c. Let (a, b), (b, c) ∈ R
Then, a = b, b = c
∴ a = c
∴ (a, c) ∈ R
∴ R is transitive.
Thus, R is an equivalence relation.
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.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.
(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.
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 implies (b, a) ∈ R
Justify your answer in case.
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.
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 is a relation from set A = (11, 12, 13) to set B = (8, 10, 12) defined by y = x − 3, then write R−1.
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.
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.
If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
Let R be a relation on N defined by x + 2y = 8. The domain of R is
Let R be a relation from a set A to a set B, then
If (x − 1, y + 4) = (1, 2) find the values of x and y
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
R7 = {(a, b)/a, b ∈ N, a + b = 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
R1 = {(1, 4), (1, 5), (1, 6)}
Answer the following:
Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}
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
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
Multiple Choice Question :
Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.
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
If R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.
Is the given relation a function? Give reasons for your answer.
h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.
Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.
Which condition must hold for a relation to be a function from \(A\) to \(B\)?
Which statement about images in a function is correct?
For a relation \(R\), the domain is the set of all:
Given \(A=\{1,2,3,4,5\}\), which relation consists of ordered pairs satisfying \(x+y=5\), where \(x,y\in A\)?
