Question

State and prove De Morgan’s first and second theorem.

Answer 1

First Theorem: The complement of the sum is equal to the product of its complements.

`overline("A" + "B") = overline"A".overline"B"`

A	B	A + B	`overline("A" + "B")`	`overline"A"`	`overline"B"`	`overline"A".overline"B"`
0	0	0	1	1	1	1
0	1	1	0	1	0	0
1	0	1	0	0	1	0
1	1	1	0	0	0	0

Second Theorem: The complement of the product of two inputs is equal to the sum of its complements.

`overline("A"."B") = overline"A" + overline"B"`

A	B	A.B	`overline("A"."B")`	`overline"A"`	`overline"B"`	`overline"A" + overline"B"`
0	0	0	1	1	1	1
0	1	0	1	1	0	1
1	0	0	1	0	1	1
1	1	1	0	0	0	0