The proposition "The night is young, and you're so...

The proposition "The night is young, and you're so beautiful" is a substitution instance of which of the following propositional forms?
1. $p$
5. $p \& q \& r$
2. $q$
6. $p \& p$
3. $p \& q$
7. $p$ or $q$
4. $p \& r$

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Key Concepts

Propositional Variables

In propositional logic, simple statements are represented by symbols like p, q, and r. These symbols stand for whole propositions and can be substituted by actual declarative sentences without changing the logical structure of the compound statement.

Substitution Instance

A substitution instance occurs when specific declarative sentences replace propositional variables in a propositional form. This concept allows us to see that a logical form like p & q becomes, for example, 'The night is young and you're so beautiful' when appropriate sentences are substituted for p and q.

Compound Proposition

A compound proposition is formed by combining two or more statements (propositional variables) using logical connectives. In the given proposition, the form is created by joining two statements with the 'and' connective, yielding the structure p & q.

Logical Connectives

Logical connectives, such as 'and', 'or', and 'not', are used to form compound statements from simpler propositions. The 'and' connective (symbolized by &) is used to construct a compound proposition that is true only when both constituent propositions are true.

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