Let \(p, q, r\) denote the statements ”It is raining”, “It is cold”, and “It…
2017
Let \(p, q, r\) denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by
Answer: A. \((\neg p \wedge r) \wedge (\neg r \rightarrow (p \wedge q))\) — Key idea: translate each clause and join them with 'and' (∧). First clause: "It is not raining and it is pleasant" → (¬p ∧ r). Second clause: "It is not…
- A.
\((\neg p \wedge r) \wedge (\neg r \rightarrow (p \wedge q))\) - B.
\((\neg p \wedge r) \wedge ((p \wedge q) \rightarrow \neg r)\) - C.
\((\neg p \wedge r) \vee ((p \wedge q) \rightarrow \neg r)\) - D.
\((\neg p \wedge r) \vee (r \rightarrow (p \wedge q))\)
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Correct answer: A
Key idea: translate each clause and join them with 'and' (∧).
First clause: "It is not raining and it is pleasant" → (¬p ∧ r).
Second clause: "It is not pleasant only if it is raining and it is cold" → (¬r) → (p ∧ q). ('Only if' means the left part implies the right part.)
Final translation: (¬p ∧ r) ∧ (¬r → (p ∧ q))
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