Question

1. read the following complex sentence.

ann eats a hamburger, and andy eats pizza.
what is the correct logical statement for the complex sentence?
○ $p \
ightarrow q$
○ $p \land q$
○ $p \lor q$
○ $p \cup q$

Explanation:

1. First, define the propositions: Let \( p \) be "Ann eats a hamburger" and \( q \) be "Andy eats pizza".
2. The sentence "Ann eats a hamburger, and Andy eats pizza" is a conjunction of two propositions, meaning both \( p \) and \( q \) are true.
3. In logical notation, the conjunction of \( p \) and \( q \) is represented as \( p \land q \).

• \( p

ightarrow q \) represents "if \( p \) then \( q \)" (implication), which does not match the "and" in the sentence.

• \( p \lor q \) represents " \( p \) or \( q \)" (disjunction), which is not the case here as the sentence is about both events happening.
• \( p \cup q \) is a set - theoretic notation (union) and not a logical connective for propositions in the context of this sentence.

Answer:

B. \( p \land q \)