1. The problem asks to identify which sentences are statements and which are not, and explain why.
2. A statement is a sentence that is either true or false, but not both.
3. a. "When is your birthday?" is a question, not a statement, because it does not have a truth value.
4. b. "I will pass in this subject." is a statement because it can be true or false, even if we don't know which.
5. c. "The number 3.2 is an even number." is a statement because it can be evaluated as true or false. In this case, it is false because 3.2 is not an integer, so it cannot be even.
6. Next, we translate sentences into symbolic logic using the given propositions:
7. Let $p$: The sun is shining.
8. Let $q$: It is raining.
9. Let $r$: The ground is wet.
10. a. "If it is raining, then the sun is not shining." translates to $q \to \neg p$.
11. b. "It is raining and the ground is wet." translates to $q \wedge r$.
12. c. "The ground is not wet." translates to $\neg r$.
13. d. "Either the sun is shining or it is raining." translates to $p \vee q$.
14. e. "The ground is wet if and only if it is raining and the sun is not shining." translates to $r \leftrightarrow (q \wedge \neg p)$.
Final answers:
- Statements: b, c
- Not statements: a
- Symbolic forms: a) $q \to \neg p$, b) $q \wedge r$, c) $\neg r$, d) $p \vee q$, e) $r \leftrightarrow (q \wedge \neg p)$
Elementary Logic A5A535
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