Based on the provided reference, the term "composite simple" does not represent a defined type of statement. The reference distinguishes between simple (or atomic) statements and composite statements, presenting them as two distinct categories. A statement is typically classified as one or the other, not both.
Let's break down the two types of statements as defined:
Simple (or Atomic) Statements
According to the reference, a simple statement is one that cannot be broken into other statements. These are the fundamental building blocks of logical expressions.
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Key Characteristic: Indivisible into smaller statements.
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Example:
- "The sky is blue."
- "Mary is a student."
- "It is raining."
These statements express a single, complete idea and do not contain any logical connectors linking multiple propositions.
Composite Statements
In contrast, a composite statement is defined as a statement that is built by using several (simple or composite statements) connected by logical expressions. These logical expressions act as operators that combine simpler ideas into more complex ones.
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Key Characteristic: Formed by combining two or more statements (simple or composite) using logical connectors.
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Common Logical Expressions (Connectors): The reference mentions examples like "if...then..."
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Other Common Connectors:
- "...and..."
- "...or..."
- "...not..."
- "...if and only if..."
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Examples:
- "If it is raining, then the ground is wet." (Connects "It is raining" and "The ground is wet" with "if...then...")
- "The sky is blue and the sun is shining." (Connects "The sky is blue" and "The sun is shining" with "...and...")
- "Mary is a student or she is a teacher." (Connects "Mary is a student" and "She is a teacher" with "...or...")
Comparing Simple vs. Composite Statements
Here's a quick comparison based on their definitions:
| Feature | Simple Statement (Atomic) | Composite Statement |
|---|---|---|
| Structure | Cannot be broken down | Built from multiple statements |
| Components | A single, complete idea | Multiple statements connected by logical expressions |
| Examples | "The cat is black." | "The cat is black and the dog is white." |
| Divisibility | Indivisible | Divisible into simpler statements |
In summary, while "composite simple" is not a recognized term within the context of the provided definition, statements are categorized as either simple (atomic) because they cannot be broken down, or composite because they are formed by combining simpler statements using logical expressions.
