Question:
If \( p : 3 \) is a prime number and \( q : \text{one plus one is three} \), then the compound statement “It is not that 3 is a prime number or it is not that one plus one is three” is:
If \( p : 3 \) is a prime number and \( q : \text{one plus one is three} \), then the compound statement “It is not that 3 is a prime number or it is not that one plus one is three” is:
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Be careful with the phrasing "It is not that (A or B)" which translates to $\sim(A \lor B)$, versus "Not A or Not B" which translates to $\sim A \lor \sim B$. The placement of "It is not that" determines the scope of the negation.
Updated On: May 2, 2026
- $\sim p \lor q$
- $\sim(p \lor q)$
- $p \land \sim q$
- $\sim p \lor \sim q$
- $p \lor \sim q$
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The Correct Option is D
Solution and Explanation
Concept:
Translating English sentences into logical symbolic form requires identifying the atomic statements and the logical connectives (negation, conjunction, disjunction).
Step 1: Identify the atomic statements.
From the question:
• $p$: "3 is a prime number"
• $q$: "one plus one is three"
Step 2: Break down the compound sentence.
The sentence is: "It is not that 3 is a prime number or it is not that one plus one is three."
• "It is not that 3 is a prime number" $\rightarrow \sim p$
• "or" $\rightarrow \lor$
• "it is not that one plus one is three" $\rightarrow \sim q$
Step 3: Combine into symbolic form.
The symbolic representation is: \[ \sim p \lor \sim q \]
Step 1: Identify the atomic statements.
From the question:
• $p$: "3 is a prime number"
• $q$: "one plus one is three"
Step 2: Break down the compound sentence.
The sentence is: "It is not that 3 is a prime number or it is not that one plus one is three."
• "It is not that 3 is a prime number" $\rightarrow \sim p$
• "or" $\rightarrow \lor$
• "it is not that one plus one is three" $\rightarrow \sim q$
Step 3: Combine into symbolic form.
The symbolic representation is: \[ \sim p \lor \sim q \]
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