Which of the following propositions is a substitution...

Which of the following propositions is a substitution instance of " $p \& q \& q$ "? 1. The night is young, and you're so beautiful, and my flight leaves in thirty minutes. 2. The night is young, and you're so beautiful, and my flight leaves in thirty minutes, and my flight leaves in thirty minutes. 3. You're so beautiful, and you're so beautiful, and you're so beautiful.

Which of the following propositions is a substitution instance of " $p \& q \& q$ "?
1. The night is young, and you're so beautiful, and my flight leaves in thirty minutes.
2. The night is young, and you're so beautiful, and my flight leaves in thirty minutes, and my flight leaves in thirty minutes.
3. You're so beautiful, and you're so beautiful, and you're so beautiful.

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Key Concepts

Propositional Logic

Propositional logic is a branch of logic that deals with propositions, which are statements that can be either true or false, and logical connectives such as 'and', 'or', and 'not'. In this context, propositional formulas are built from atomic propositions and combined using these connectives.

Substitution Instance

A substitution instance is a formula that results from taking a given propositional formula and uniformly replacing its atomic propositions with other propositions. This process must respect the structure of the original formula, meaning that if an atomic variable appears multiple times, all instances must be replaced by the same proposition.

Formula Structure and Repetition

The structure of a formula is determined by the arrangement of its logical connectives and atomic propositions. When an atomic proposition appears more than once in a formula, such as 'q' in 'p & q & q', any substitution for that atom must be applied consistently across all occurrences to maintain the intended logical relationships.

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