Question

If $p$ : It is raining and $q$ : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is

• A. $\sim p \wedge q$
• B. $\sim p \vee q$
• C. $(\sim p) \wedge (\sim q)$
• D. $(\sim p) \vee (\sim q)$

Hint:

Always memorize this phrase translation template for logic exams: "Neither $p$ nor $q$" translates directly to $\sim p \wedge \sim q$. It helps to think of it as "not $p$ AND not $q$".

Answer 1

The Correct Option is C

Step 1: Identify the simple statements.
$p$: It is raining; $q$: It is pleasant. We must symbolise It is neither raining nor pleasant.
Step 2: Read the everyday meaning.
Neither A nor B asserts that A does not happen and B does not happen at the same time.
Step 3: Negate each part.
Not raining is $\sim p$; not pleasant is $\sim q$.
Step 4: Join with and.
Both must hold together, so we use conjunction: $(\sim p) \wedge (\sim q)$.
Step 5: Cross-check with De Morgan.
By De Morgan's law $(\sim p)\wedge(\sim q) \equiv \sim(p\vee q)$, which reads it is not the case that it is raining or pleasant, exactly the given sentence.
Step 6: Conclude.
The two viewpoints agree, confirming the conjunction form.
\[ \boxed{(\sim p) \wedge (\sim q)} \]