Assignment For 1st year Natural Science Students (25%)
1. For the argument given below
a. Write argument forms.
b. Check the validity.
 If he studies medicine, he will get a good job. If he gets a good job, he
will get a good wage. He did not get a good wage. Therefore, he did
not study medicine.
2. For any two subsets
and
of a universal set
, prove that:

3. Let
and
defined by
4. Let
. Show that
is a one to one function from
then show that
onto
.
has an inverse and if it has find the
inverse.
5. If f is a real function defined by f ( x ) 
x 1
3 f ( x)  1
. Show that f (2 x ) 
.
x 1
f ( x)  3
6. Suppose that f and g be real valued functions. Then find f and g so that
2 f  3g  12x 3  5 x 2  7 x  14 and 3 f  2 g  8 x 3  2 x  6 .
7. Show that the equation | z  z 0 | r which is a circle of radius r centered at z 0
can be written as | z |2 2 Re( z z) | z 0 | 2  r 2 .
8. Show that 1  z  z 2    z n 
9. Solve the equation
1  z n 1
, for z  1.
1 z