Introduction to Boolean Logic

Introduction to Boolean Logic

Boolean logic, named after the mathematician George Boole, is a fundamental concept in computer science and mathematics. It's a system of logic that deals with truth values, which are typically represented as True (1) or False (0). Boolean logic uses logical operators to combine these truth values and produce new truth values.

Basic Logical Operators

Here are the three primary logical operators:

• AND: Represented by the symbol "?" or the word "AND". The result is True only if both operands are True. True AND True = True True AND False = False False AND True = False False AND False = False
• OR: Represented by the symbol "?" or the word "OR". The result is True if at least one operand is True. True OR True = True True OR False = True False OR True = True False OR False = False
• NOT: Represented by the symbol "¬" or the word "NOT". It inverts the truth value of its operand. NOT True = False NOT False = True

Truth Tables

A truth table is a useful way to visualize the results of logical operators for all possible combinations of input values.

AND Truth Table:

OR Truth Table:

NOT Truth Table:

Example

Let's analyze a simple expression:

(A AND B) OR (NOT C)

To evaluate this expression, we need to know the truth values of A, B, and C. Let's assume:

• A = True
• B = False
• C = True

Now, we can break down the expression:

1. (A AND B) = (True AND False) = False
2. (NOT C) = (NOT True) = False
3. (False OR False) = False

Therefore, the entire expression evaluates to False.

Applications

Boolean logic is crucial in various fields:

• Computer Science: Used in programming, circuit design, and data analysis.
• Mathematics: Foundation for set theory and logic.
• Artificial Intelligence: Used in decision-making and problem-solving.

By understanding Boolean logic, you gain the ability to represent and manipulate information efficiently, making it a valuable tool for various applications.