**8. Find the following values of the greatest integer function.
(a) [-1/4]
(b) [-22/7]
(c) [5/4]
(d) [[1/2]]
(e) [[3/2] + [-3/2]]
(f) [3 – [1/2]]
**

**Solution: **The greatest integer, denoted by [x], is the largest integer less than or equal to x satisfying the inequation

[x] \leq x<[x]+1

Where x is a real number

**(a)**[-1/4]

The greatest integer less than equal to -1/4 is -1

So, [-1/4]=1

**(b)** [-22/7]

The greatest integer less than equal to -22/7 is -4

So, [-22/7]=-4

**(c)** [5/4]

The greatest integer less than equal to 5/4 is 1

So, [5/4]=1

**(d)** [[1/2]]

The greatest integer less than equal to 1/2 is 0

Now, [[1/2]]=[0]

=0

So, [[1/2]]=0

**(e)** [[3/2]+[-3/2]]

The greatest integer less than equal to 3/2 is 1

So, [3/2]=1

Also, the greatest integer less than equal to -3/2 is -2

Now,

[[3/2]+[-3/2]]=[1+(-2)]

=[-1]

=-1

So, [[3/2]+[-3/2]]=-1

**(f)** [3-[1/2]]

The greatest integer less than equal to 1/2 is 0

So, [1/2]=0

Now,

[3-[1/2]]=[3-0]

=[3]

=3

So, [3-[1/2]]=3