Questions: Is the argument valid?

Solution Steps

• The given truth table includes two propositions \( p \) and \( q \).
• The table shows the truth values for \( p \), \( q \), \( \neg p \), \( \neg q \), \( p \land q \), \( p \lor q \), \( \neg p \lor \neg q \), and \( (p \land q) \rightarrow \neg (p \lor q) \).

• The truth table provides the truth values for each combination of \( p \) and \( q \):
  • \( p \) and \( q \) both true (T, T)
  • \( p \) true and \( q \) false (T, F)
  • \( p \) false and \( q \) true (F, T)
  • \( p \) and \( q \) both false (F, F)

• To determine if the argument is valid, we need to check if the conditional statement \( (p \land q) \rightarrow \neg (p \lor q) \) is true in all cases.
• From the truth table:
  • When \( p \) and \( q \) are both true, \( (p \land q) \) is true and \( \neg (p \lor q) \) is false, making the conditional false.
  • In all other cases, the conditional is true.

Final Answer