Which expression represents the disjunction of P and Q?

Which expression represents the disjunction of P and Q?

• A. P and Q
• B. P or Q
• C. Q -> P
• D. Not P -> Q

Answer: (B)

Disjunction in logic means at least one of the statements is true. When you form the expression with P or Q, it is true in every case where P is true, or Q is true, or both are true. The only time it’s false is when neither P nor Q is true. This matches the intuition of "or" as a choice between possibilities that includes the possibility of both being true. The other forms aren’t disjunction: P and Q requires both to be true; Q implies P and Not P implies Q are conditional statements with their own distinct truth patterns. Therefore, the expression that captures disjunction is P or Q.

Disjunction in logic means at least one of the statements is true. When you form the expression with P or Q, it is true in every case where P is true, or Q is true, or both are true. The only time it’s false is when neither P nor Q is true.

This matches the intuition of "or" as a choice between possibilities that includes the possibility of both being true. The other forms aren’t disjunction: P and Q requires both to be true; Q implies P and Not P implies Q are conditional statements with their own distinct truth patterns. Therefore, the expression that captures disjunction is P or Q.