Day 43: Boolean Algebra
Hello Dear Students,
Hope you all are doing good...
So, aaj hum boolean algebra topic ko cover karenge,
Let's get started...
BOOLEAN ALGEBRA -
- Boolean Algebra was first developed by George Boole in 1854, but the formal definition was given by E.V.Huntington in 1904.
- Boolean ka matlab hota hai true or false, here 0 and 1.
- Boolean Algebra is a branch of mathematics algebra.
- Boolean algebra is set of 3 operations which are-
- + (similar to logical OR), also denoted as ∨
- ・(similar to logical AND), also denoted as ∧
- ー (NOT), also denoted as prefix ᄀ
- There are only 2 values i.e. 0 and 1, agar hum koi bhi operation perform karenge so uska result 0 and 1 mein hi ayega, whether 0, 1, or combination of 0 and 1.
The Truth Table of these 3 operations, AND, OR, NOT as as follows-
- Truth Table for AND
| A | B | R |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
- Truth Table for OR
| A | B | R |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
- Truth Table for NOT
| A | R |
| 0 | 1 |
| 1 | 0 |
- PRECEDENCE OF BOOLEAN OPERATIONS
| Operator | Symbol | Precedence |
| Parenthesis | ( ) | First Priority for solving Parenthesis |
| AND | ・ | Highest |
| OR | + | Middle |
| NOT | ー | Lowest |
- Duality Principle - Duality principle is very simple. In this, replace 0 with 1 and 1 with 0. And also replace + with ・, and ・ with +.
- Note that, because boolean algebra has only 2 values, 0 and 1, then the complement of 1 is 0, and the complement of 0 is 1.
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UGC NET EXPERTS