\[
\text { (3) Given: } \begin{aligned}
& d \rightarrow e \\
& d \vee f \\
& h \rightarrow \sim e \\
& h
\end{aligned}
\]
Prove: \( f \)

Answer

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Answer

\(7. f \) (5, 6, Disjunctive Syllogism)

Steps

Step 1 ：\(1. h \rightarrow \sim e \) (Given)

Step 2 ：\(2. h \) (Given)

Step 3 ：\(3. \sim e \) (1, 2, Modus Ponens)

Step 4 ：\(4. d \rightarrow e \) (Given)

Step 5 ：\(5. \sim d \) (3, 4, Modus Tollens)

Step 6 ：\(6. d \vee f \) (Given)

Step 7 ：\(7. f \) (5, 6, Disjunctive Syllogism)