Question

The tautology \[ \bigl(p \wedge (p \rightarrow q)\bigr) \rightarrow q \] is the basis of the following rule of inference:

• A. Modus Ponens
• B. Modus Tollens
• C. De Morgan Law
• D. Morgan Tonen

Hint:

Modus Ponens: [ p,parrow q \Longrightarrow q ] is the most frequently used rule of inference in propositional logic.

Answer 1

The Correct Option is A

Concept: A rule of inference is a valid logical argument form used to derive conclusions from premises. One of the most important rules is Modus Ponens: [ p,parrow q ] Therefore, [ q. ] The tautology [ (p\wedge(parrow q))arrow q ] expresses exactly this reasoning.

Step 1: Interpret the expression. The statement [ p\wedge(parrow q) ] means both (p) and (parrow q) are true.

Step 2: Apply logical implication. If (p) is true and [ parrow q ] is true, then (q) must also be true.

Step 3: Recognize the inference rule. This is exactly the rule: [ p,; parrow q \Longrightarrow q. ] This rule is called Modus Ponens. [ Modus Ponens ]