Question

Prove by perfect induction the deMorgan formula for this,

A-B=(A + B)

Answer 1

The deMorgan formula :-

$\overline{A . B} = \overline{A} + \overline{B}$

Iin Boolean Algebra the variables have only two possible values: 0 and 1

Now prove of the deMorgan formula from perfect induction :-

A	B	A.B	A+B	(A.B)'	(A+B)'	A'	B'	A' + B'
0	0	0	0	1	1	1	1	1
0	1	0	1	1	0	1	0	1
1	0	0	1	1	0	0	1	1
1	1	1	1	0	0	0	0	0

From that table we can say that

$\overline{A . B} = \overline{A} + \overline{B}$

becasue coloum 5 and 9 are same, and thus, by perfect induction, both expressions are equivalent.

but expression

$\overline{A . B} = \overline{A + B}$

are not same from coloum 5 and 6 in the table.