Advertisements
Advertisements
प्रश्न
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?
पर्याय
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
उत्तर
Statement 1 is true only if Statement 2 is true.
APPEARS IN
संबंधित प्रश्न
Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.
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.
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
The following relation is defined on the set of real numbers.
aRb if 1 + ab > 0
Find whether relation is reflexive, symmetric or transitive.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
Give an example of a relation which is reflexive and symmetric but not transitive?
Give an example of a relation which is transitive but neither reflexive nor symmetric?
Show that the relation R defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.
If R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?
Let C be the set of all complex numbers and C0 be the set of all no-zero complex numbers. Let a relation R on C0 be defined as
`z_1 R z_2 ⇔ (z_1 -z_2)/(z_1 + z_2)` is real for all z1, z2 ∈ C0.
Show that R is an equivalence relation.
If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.
Let R = {(x, y) : |x2 − y2| <1) be a relation on set A = {1, 2, 3, 4, 5}. Write R as a set of ordered pairs.
Define an equivalence relation ?
For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.
Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs
Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .
If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is _____________ .
If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective
Give an example of a map which is neither one-one nor onto
Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.
Which of the following is not an equivalence relation on I, the set of integers: x, y
Let `"f"("x") = ("x" - 1)/("x" + 1),` then f(f(x)) is ____________.
Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.
Given set A = {a, b, c}. An identity relation in set A is ____________.
Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.
Answer the following using the above information.
- Let relation R be defined by R = {(L1, L2): L1║L2 where L1, L2 ∈ L} then R is ____________ relation.
If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is
Let A = {3, 5}. Then number of reflexive relations on A is ______.
