Vhich of the following combination of propositions \( p \) and \( q \) is true when at least one of them is rue? \( p \vee q \) \( p \wedge q \) \( p \Rightarrow q \) \( p \oplus q \)

To determine which of the given combinations of propositions \( p \) and \( q \) is true when at least one of them is true, let's analyze each option: 1. **\( p \vee q \)** (Logical OR): This proposition is true if at least one of \( p \) or \( q \) is true. Therefore, if at least one of them is true, \( p \vee q \) is true. 2. **\( p \wedge q \)** (Logical AND): This proposition is true only if both \( p \) and \( q \) are true. If at least one of them is true but not both, \( p \wedge q \) will be false. 3. **\( p \Rightarrow q \)** (Logical Implication): This proposition is true in all cases except when \( p \) is true and \( q \) is false. Therefore, if at least one of them is true, \( p \Rightarrow q \) may or may not be true depending on the truth values of \( p \) and \( q \). 4. **\( p \oplus q \)** (Logical XOR): This proposition is true if exactly one of \( p \) or \( q \) is true. If both are true or both are false, \( p \oplus q \) is false. Therefore, it is not guaranteed to be true when at least one of them is true. From this analysis, the only combination that is guaranteed to be true when at least one of \( p \) or \( q \) is true is: **\( p \vee q \)**.