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
A.
2n + 1
A relation on set A is a subset of A A.
Let A= {a1, a2, a3, ..., an}. Then, a reflexive relation on A must contain atleast n elements
(a1,a1), (a2, a2) ... (an, an).
Number of reflexive relations on A is .
Clearly, n2 - n = n, n2 - n = n - 1, n2 - n = n2 - 1 have solutions in N but n2 - n = n + 1 does not have solutions in N.
So, 2n + 1 cannot be the number of reflexive relations on A.
If A and B be two sets such that A x B consists of 6 elements. If three elements A x B are (1, 4), (2, 6) and (3, 6), find B x A.
{(1, 4), (1, 6), (2, 4), (2, 6), (3, 4), (3, 6)}
{(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
{(4, 4), (6, 6)}
{(4, 1), (6, 2), (6, 3)}
The solution set contained in R of the inequation
3x + 31 - x - 4 < 0, is:
(1, 3)
(0, 1)
(1, 2)
(0, 2)
If N denotes the set of all positive integers and if f : efined by f(n) = the sum of positive divisors of n then, f(2k, 3), where k is a positive integers, is
2k + 1 - 1
2(2k + 1 - 1)
3(2k + 1 - 1)
4(2k + 1 - 1)
If f : R R is defined by f(x)=x - [ x] - for x R, where [x] is the greatest mteger not exceeding x, then is equal to :
Z, the set of all integers
N, the set of all natural numbers
, the empty set
R