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# Proof of De-Morgan’s laws in boolean algebra

• Difficulty Level : Easy
• Last Updated : 14 May, 2020

Statements :
1.
2.

Proof:
Here we can see that we need to prove that the two propositions are complement to each other.
We know that and which are annihilation laws. Thus if we prove these conditions for the above statements of the laws then we shall prove that they are complement of each other.

For statement 1:
We need to prove that:
and

Case 1.

{Using distributive property}

Hence proved.

Case 2.

Hence proved.

For statement 2:
We need to prove that:
and

Case 1.

{We know that A+BC=(A+B).(A+C)}

Hence proved.

Case 2.

Hence Proved.
This proves the De-Morganâ€™s theorems using identities of Boolean Algebra.

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