Question

Write the statement in symbolic form 'Sandeep neither likes tea nor coffee but enjoys a soft drink'. Where \( p \): Sandeep likes tea, \( q \): Sandeep likes coffee, \( r \): Sandeep enjoys a soft drink

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

Hint:

When translating English statements into symbolic logic, break the statement into simpler parts and represent them using conjunctions and disjunctions.

Answer 1

The Correct Option is B

Step 1: Break down the statement.
The statement "Sandeep neither likes tea nor coffee but enjoys a soft drink" means: - \( \neg p \): Sandeep does not like tea. - \( \neg q \): Sandeep does not like coffee. - \( r \): Sandeep enjoys a soft drink. Step 2: Express in symbolic form.
The logical conjunction of "neither likes tea nor coffee" is \( \neg p \land \neg q \), and since "enjoys a soft drink" is \( r \), the full statement is: \[ (\neg p \land \neg q) \land r \] Step 3: Conclusion.
The correct answer is (B) \( (\neg p \land \neg q) \land r \).