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
B.
The range is
C.
The domain is
We have,
Domain = R - {f(x) = 0}
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
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