**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-Morgan’s theorems using identities of Boolean Algebra.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Properties of Boolean Algebra
- Basic Laws for Various Arithmetic Operations
- Proof that vertex cover is NP complete
- Computer Organization | Amdahl's law and its proof
- RENAME (ρ) Operation in Relational Algebra
- Basis Vectors in Linear Algebra - ML
- Set Theory Operations in Relational Algebra
- SELECT Operation in Relational Algebra
- PROJECT Operation in Relational Algebra
- Orthogonal and Orthonormal Vectors in Linear Algebra
- Cartesian Product Operation in Relational Algebra
- How to solve Relational Algebra problems for GATE
- Boolean Algebraic Theorems
- Representation of Boolean Functions
- Minimization of Boolean Functions
- Number of Boolean functions
- Counting Boolean function with some variables
- Prime Implicant chart for minimizing Cyclic Boolean functions
- Difference between Relational Algebra and Relational Calculus

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.