The Rule of Addition in Logic

The rule of addition in logic is a simple but important rule of inference. It states that if a statement (proposition) is true, then you can infer that this statement is true even when combined with any other statement using the logical OR operator (denoted as ∨).

Rule:

If P is true, then P ∨ Q is also true, regardless of what Q is.

Formal Representation:

P
P ∨ Q

Where:

• P and Q are propositions.
• ∨ is the logical OR operator.

Explanation:

The rule of addition follows from the truth table of the logical OR operator. In propositional logic, for any two propositions P and Q, the statement P ∨ Q is true if at least one of P or Q is true. Since we know P is true, it doesn't matter what Q is—whether Q is true or false, the entire expression P ∨ Q will still be true.