| (a) |
(i) How many functions are there from a set with
three elements to a set with four elements? Explain your answer. |
[2] |
|
(ii) How many functions are there from a set
with four elements to a set with three elements? Explain your answer. |
[2] |
| (b) |
(i) How many one-to-one functions are
there from a set with three elements to a set with four elements? Explain your answer. |
[2] |
|
(ii) How many one-to-one functions are
there from a set with four elements to a set with three elements? Explain your answer. |
[2] |
| (c) |
(i) How many onto functions are there
from a set with three elements to a set with four elements? Explain your answer. |
[2] |
|
(ii) How many onto functions are there
from a set with four elements to a set with three elements? Explain your answer. |
[2] |
| (d) |
(i) How many invertible functions are
there from a set with three elements to a set with four elements? |
[1] |
|
(ii) How many invertible functions are
there from a set with four elements to a set with three elements? |
[1] |
| (e) |
Construct a function from three elements to two
elements which is neither one-to-one nor onto. |
[2] |
| (f) |
The relation R, "is a factor of
" is defined on  . Decide whether or not R
is reflexive, symmetric or transitive. |
[4] |