Advertisements
Advertisements
Question
Statement 1: The intersection of two equivalence relations is always an equivalence relation.
Statement 2: The Union of two equivalence relations is always an equivalence relation.
Which one of the following is correct?
Options
Statement 1 implies Statement 2.
Statement 2 implies Statement 1.
Statement 1 is true only if Statement 2 is true.
Statement 1 and 2 are independent of each other.
Advertisements
Solution
Statement 1 is true only if Statement 2 is true.
APPEARS IN
RELATED QUESTIONS
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
Given an example of a relation. Which is reflexive and transitive but not symmetric.
Given an example of a relation. Which is symmetric and transitive but not reflexive.
Let L be the set of all lines in the XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
Defines a relation on N:
x + 4y = 10, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?
Write the smallest equivalence relation on the set A = {1, 2, 3} ?
Mark the correct alternative in the following question:
The relation S defined on the set R of all real number by the rule aSb if a b is _______________ .
Mark the correct alternative in the following question:
The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .
Show that the relation S in the set A = [x ∈ Z : 0 ≤ x ≤ 12] given by S = [(a, b) : a, b ∈ Z, ∣a − b∣ is divisible by 3] is an equivalence relation.
If A = {a, b, c}, B = (x , y} find B × B.
Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, symmetric and transitive
Give an example of a map which is neither one-one nor onto
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is ______.
Let A = {1, 2, 3}, then the relation R = {(1, 1), (1, 2), (2, 1)} on A is ____________.
Given set A = {1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be ____________.
Which statement defines a Universal Relation?
What should be checked to determine whether a relation is symmetric?
