Relations-and-Functions

Question 1
The number of onto function (surjective function) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is ______.
A
36
B
37
C
38
D
39
       Engineering-Mathematics       Relations-and-Functions       GATE 2015 -(Set-2)
Question 1 Explanation: 
Number of onto function from set X to set Y with |X| = m, |Y| = n is

m = 4, n = 3 ⇒ number of onto function is
Question 2
Let S denote the set of all functions  f:{0,1}→ {0,1}. Denote by N the number of functions from S to the set {0,1}. The value of loglog2N is ______.
A
16
B
17
C
18
D
19
       Engineering-Mathematics       Relations-and-Functions       GATE 2014(Set-01)
Question 2 Explanation: 
The number of functions from A to B where size of A=|A| and size of B=|B| is |B||A|
{0,1}4={0,1}×{0,1}×{0,1}×{0,1}=16
|S|=216
N=2|S|
loglogN=loglog2|S|=log |S| =log216=16
There are 2 questions to complete.