# Introduction to Logic Structures

## Logic

Definitions:
Logic is the study of the principles and methods that distinguish between a valid and an invalid argument.
Statement is a declarative sentence that is either true (T) or false (F) but not both. A statement is also referred to as a proposition.
Examples:
• 3+4 = 7.
• It is Friday today.

If a proposition is true, we say that it has a truth value of "True". If a proposition is false, its truth value is "falseQuot. The truth values "true" and "false" are, respectively, denoted by the letters T and F.

Examples:
• "4 + 3 = 7" and "Sevilla is a city in Spain"
• "The grass is green" or " It is sunny today"
• "Computer Science is not difficult to me"
AND, OR, NOT are called Logical Connectives.

## Symbolic Representation

Statements are symbolically represented by letters such as P, p, q, r, s, T, . . .
Examples:
• P = "Rome is the capital of Italy".
• q ="20 is divisible by 3".
The table below shows the details of logic connectivity Examples
• p= "Cairo is the capital of Egypt".
• q="16 is divisible by 3".
• P ∧ q =" Cairo is the capital of Egypt and 16 is divisible by 3".
• P ∨q="Cairo is the capital of Egypt or 16 is divisible by 3".
• ~P = "It is not the case that Cairo is the capital of Egypt" or simply "Cairo is not the capital of Egypt".
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Date of last modification: February 7, 2019