Multiply through by  we have

Reordering the equation we have

Factorizing we have

Solving we have  or
If  then
If  then  or

Multiplying through by , we have
So
Factorizing we have
Solving we have  of
If
sine
 hn sha inle
1e

Let .
Factorizing we have

So  or

Also  or  is not real

.
We can express the given equation thus.
 
Now let
Factorizing we have
Hence  or
,
If
If  then  i.e.  is undefined

Simplifying the equation we have

Let  then
Dividing through by 2 the common factor to the terms,

Factorizing we have
Hence  or
But , so  or
Therefore  or  i.e.  is undefined.

We rewrite the equation thus:

Let  then
Factorizing we have

 or
But
Hence  or
If , then
Also if  (  is undefined or  is notareal number)

We express the equation as

Let
Factorising we have
 or
 or
But , so  or
Considering
We apply logarithms thus


If  then,  which means no real number satishes the equation.

, then
Factorising, we have

 or
But  or   or
By comparison of powers we have  or

(i)

(ii)
(iii)

a)

From the table above the last two columns are identical. Hence ∼p∧∼q and ∼(p∨q) are logically equivalent
b)

The last two columns of the table above are identical. Hence ∼(p∧q) and ∼p∨∼q are logically equivalent