Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then
A is not transitive
R is symmetric only
R is an equivalence relation
R is not an equivalence relation
For the function f(x) = . where [x] denotes the greatest integer less than or equal to x, which of the following statements are true?
The domain is
The range is
The domain is
The range is
If R be the set of all real numbers and f : R ➔ R is given by f(x) = 3x2 + 1. Then, the set f-1([1, 6]) is
If f(x) = 2100x + 1, g(x) = 3100x + 1, then the set ofreal numbers x such that f{g(x)} = x is
empty
a singleton
a finite set with more than one element
infinite
Three sets A, B, C are such that A = B ∩ C and B = C ∩ A, then
A ⊂ B
A ⊃ B
A ≡ B
A ⊂ B'
C.
A ≡ B
Since, A = B ∩ C and B = C ∩ A, then A ≡ B
If A = {x : x2 - 5x + 6 = 0}, B={2, 4}, C = {4, 5}, then A x (B ∩ C) is
{(2, 4), (3, 4)}
{(4, 2), (4, 3)}
{(2, 4), (3, 4), (4, 4)}
{(2, 2), (3, 3), (4, 4), (5, 5)}
Let A and B be two non-empty sets having n elements in common. Then, the number of elements common to A x B and B x A is
2n
n
n2
None of these
If a set A contains n elements, then which of the following. cannot be the number of reflexive relations on the set A?
2n + 1
2n - 1
2n