In Hypothetical Propositions you met statements built from other statements: "If it rains, then the game is canceled" contains two smaller claims. Symbolic logic starts by taking that idea seriously. Before we can write any symbols, we have to know which pieces of a sentence are the building blocks.
A simple statement makes one claim and has no other statement inside it: "Maya is at the park." A compound statement is built from one or more simpler statements with a word like not, and, or, if … then or if and only if: "Maya is at the park and Leo is at home."
Key idea
Why it works
Worked examples
Worked example: Find the simple parts
- Look for a connective word: "either … or".
- It joins two claims: "the library is open" and "the bookstore is open".
- Each of those has no smaller statement inside it, so each is simple.
Answer: Compound, with two simple parts.
Worked example: One relation, not two claims
- The word "and" appears, so check what it joins.
- Try splitting: "Ava is a cousin and Ben is a cousin." That is not what the sentence says; "cousin" needs someone to be a cousin of.
- The sentence states one relation between two people. "And" joins two names, not two statements.
Answer: Simple.
Worked example: A hidden "not"
- "Un-" is part of the word "unhappy", not the connective "not".
- There is no smaller statement inside it.
Answer: Simple.
Common mistake
- Look for the connective words: not, and, but, or, either … or, neither … nor, if … then, only if, unless, if and only if.
- Check that each connective joins whole statements, not just names or words.
- Count a negation as compound, with one part.