I have just started learning introductory discrete math and I am kind of confused. I can't see the difference between compound statements and statement forms. To me, they look the same according two these 2 definitions:
Compound statement:
A statement represented by a some combination of statement variables and connectives is called a compound statement.
Statement form:
Statement form or propositional form is an expression made up of statement variables such as p, q, r and logical connectives that becomes a statement when actual statements are substituted for the component statement variables.
Are they the same thing ? What am I missing here?
Best Answer
A compound statement: "It is raining, and if I don't find my umbrella, I will stay at home."
A statement form corresponding to the above: $r\land(\neg f \to s)$.
A statement that is not compound: "It is raining."
A statement form corresponding to the non-compound statement: $r$.
Don't sweat this too much. Once you get to leave the natural-language sentences behind and just focus on the mathematics, both of these concepts will mostly fade back into obscurity, and it will suddenly be okay to call $r\land (\neg f\to s)$ a statement anyway.