Advertisements
Advertisements
Question
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 equivalence
Advertisements
Solution
Given A = {a, b, c}
R = {(a, a), (b, b), (a, c)}
After including the ordered pairs (c, c), (c, a) to R the new relation becomes
R1 = {(a, a), (b, b), (c, c), (a, c), (c, a)}
R1 is reflexive symmetric and transitive.
∴ R1 is an equivalence relation.
APPEARS IN
RELATED QUESTIONS
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
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 from a set A to a set B, then
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:
Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.
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?
R3 = {(2, –1), (7, 7), (1, 3)}
Discuss the following relation for reflexivity, symmetricity and transitivity:
The relation R defined on the set of all positive integers by “mRn if m divides n”
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 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 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 equivalence
Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.
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.
t = {(x, 3) | x is a real number
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 ______.
Which statement defines a relation from set \(A\) to set \(B\)?
Which statement about images in a function is correct?
