A formal proof has the lines P→ Q and P, both allowed hypotheses. Which line can legitimately be added?

Q, by modus ponens on the earlier lines

R, because the reader intuits it

Exercise · ZW-FORMAL-PROOF-009 · ★★★ Advanced

A formal proof has the lines \(P\to Q\) and \(P\), both allowed hypotheses. Which line can legitimately be added?

Choose one option.

Show answer

D. \(Q\), by modus ponens on the earlier lines

Explanation

Modus ponens applied to \(P\to Q\) and \(P\) yields \(Q\), which is justified by that rule. The other options have no valid rule supporting them.

Open the ZWMath map →

Review the concept: Formal proof

A formal proof of \(\varphi_n\) is a sequence \(\varphi_1,\ldots,\varphi_n\) in which each term is an axiom, an admitted hypothesis, or the result of a rule applied to earlier terms.

\[\varphi_1,\varphi_2,\ldots,\varphi_n\vdash\varphi_n\]

A formal proof has the lines \(P\to Q\) and \(P\), both allowed hypotheses. Which line can legitimately be added?

Explanation

Review the concept: Formal proof

More practice problems: formal proof