# Mathematics | Properties of Boolean algebra

**Switching algebra** is also known as ** Boolean Algebra**. It is used to analyze digital gates and circuits It is logic to perform mathematical operation on binary numbers i.e., on ‘0’ and ‘1’. Boolean Algebra contains basic operators like AND, OR and NOT etc. Operations are represented by ‘.’ for AND , ‘+’ for OR . Operations can be performed on variables which are represented using capital letter eg ‘A’ , ‘B’ etc.

** Properties of switching algebra –**

**Annulment law –**a variable ANDed with 0 gives 0, while a variable ORed with 1 gives 1, i.e.,A.0 = 0

A + 1 = 1**Identity law –**in this law variable remain unchanged it is ORed with ‘0’ or ANDed with ‘1’, i.e.,A.1 = A

A + 0 = A**Idempotent law –**a variable remain unchanged when it is ORed or ANDed with itself, i.e.,A + A = A

A.A = A**Complement law –**in this Law if a complement is added to a variable it gives one, if a variable is multiplied with its complement it results in ‘0’, i.e.,A + A’ = 1

A.A’ = 0**Double negation law –**a variable with two negation its symbol gets cancelled out and original variable is obtained, i.e.,((A)’)’=A

**Commutative law –**a variable order does not matter in this law, i.e.,A + B = B + A

A.B = B.A**Associative law –**the order of operation does not matter if the priority of variables are same like ‘*’ and ‘/’, i.e.,A+(B+C) = (A+B)+C

A.(B.C) = (A.B).C**Distributive law –**this law governs opening up of brackets, i.e.,A.(B+C) = (A.B)+(A.C)

A+(B.C) = (A+B).(A+C)**Absorption law –**:-This law involved absorbing the similar variables, i.e.,A.(A+B) = A

A + AB = A**De Morgan law –**the operation of an AND or OR logic circuit is unchanged if all inputs are inverted, the operator is changed from AND to OR, the output is inverted, i.e.,(A.B)’ = A’ + B’

(A+B)’ = A’.B’- Mathematics | Power Set and its Properties
- Mathematics | Representation of Boolean Functions
- Properties of Determinants of Matrices
- Properties of Asymptotic Notations
- ACID Properties in DBMS
- Properties of Relational Decomposition
- Rough Set Theory | Properties and Important Terms | Set - 2
- Counting Boolean function with some variables
- Digital Logic | Minimization of Boolean Functions
- Digital Logic | Number of Boolean functions
- Prime Implicant chart for minimizing Cyclic Boolean functions
- How to solve Relational Algebra problems for GATE
- Mathematics | Generalized PnC Set 1
- Mathematics | Generalized PnC Set 2
- Mathematics | Probability

**GATE CS Corner Questions**

Practicing the following questions will help you test your knowledge. All questions have been asked in GATE in previous years or in GATE Mock Tests. It is highly recommended that you practice them.

**References –**

Boolean algebra – Wikipedia

De Morgan’s laws – Wikipedia

This article is contributed by **Vaishali Bhatia**. 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 write comments if you find anything incorrect, or you want to share more information about the topic discussed above.