Advertisements
Advertisements
प्रश्न
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
Advertisements
उत्तर
(a) S = aRa
Reflexivity would require aFa for every person a ∈ P, i.e., “everyone is a friend of themselves.” In ordinary usage, a person is not considered a friend of themselves. Hence a`\cancelF`a for all a, so F is not reflexive.
(b) aRb ⇒ bRa so it is symmetric
(c) aRb, bRc does not
⇒ aRc so it is not transitive
⇒ It is not an equivalence relation
APPEARS IN
संबंधित प्रश्न
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}}.
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
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.
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
If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is
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 `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y
Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)
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:
Determine the domain and range of the following relation.
R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}
Discuss the following relation for reflexivity, symmetricity and transitivity:
On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”
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
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 reflexive
Choose the correct alternative:
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
