Item 3.1.15.b.
Prove that the following is a valid deduction rule for any \(n \ge 2\text{:}\)
| \(P_1 \imp P_2\) | |
| \(P_2 \imp P_3\) | |
| \(\vdots\) | |
| \(P_{n-1} \imp P_n\) | |
| \(\therefore\) | \(P_1 \imp P_n\text{.}\) |
I suggest you don't go through the trouble of writing out a \(2^n\) row truth table. Instead, you should use part (a) and mathematical induction.