Question

Write a note on De Morgan’s Theorems to prove it.

Answer 1

Theorem (a): De Morgan’s Theorems: (x + y)’ = x’. y’

Proof: The truth table for proving this theorem is given below:From the truth table, it is clear that both sides of the theorem are equal. Hence, the theorem is proved.

Theorem (b): (x + y)’ = x’ + y’

Proof: The truth table for proving this theorem is given below: From the truth table, It is clear that both sides of the theorem are equal. Hence, the theorem is proved.

Theorems 6(a) and 6(b) are very important and useful. They are known as De Morgan’s theorems. They can be extended to n variables as given below:

(X₁ + X₂ + X₃ + ………. + X_n )’ = X_{1 ‘} . X _2‘ . X_{3 ‘} …….. X_{n ‘}

(X₁. X₂ . X₃ . …… X_n )’ = X_{1 ‘} + X_2’ + X_{3 ‘} + ……….. + X_{n ‘}