Question

If \( p \): He is intelligent, \( q \): He is strong. Then, symbolic form of statement "It is wrong that he is intelligent or strong" is:

• A. \( \sim p \lor \sim q \)
• B. \( \sim(p \land q) \)
• C. \( \sim(p \lor q) \)
• D. \( p \lor \sim q \)

Hint:

When translating from English to symbolic logic, pay close attention to phrases that indicate grouping. "It is wrong that..." negates the entire clause that follows, requiring parentheses around the expression being negated.

Answer 1

The Correct Option is C

Step 1: Identify the individual logical statements, which are \( p \): "He is intelligent" and \( q \): "He is strong".
Step 2: Translate the phrase "he is intelligent or strong". The logical operator for "or" is disjunction (\( \lor \)). Thus, this phrase becomes \( p \lor q \).
Step 3: Translate the negation "It is wrong that...". This corresponds to the negation operator (\( \sim \)) applied to the entire statement that follows.
Step 4: Combine the parts. Applying the negation to the expression from Step 2 gives \( \sim(p \lor q) \).