Logic Exercise: PD James "The Victim" (1973)

Inspired by PD James, “The Victim” (1973)

[1] The threatening notes are to be untraceable and if so, then I wear gloves while composing them. [2] Either I write them or I type them or I cut-and-paste letters from cut-up newspapers. [3] But if I write them, they’re not untraceable; and I can’t both wear gloves and cut-and-paste letters from cut-up newspapers. So I must type them.

Let:      C = I cut-and-paste them

            G = I wear gloves

            T = I type them

            U = The notes are to be untraceable

            W = I write them

Represent the argument and prove the conclusioin

Solution:

(1)      U & (U → G)                           Premise

(2)      W v T v C                                Premise

(3)      (W → ~U) & ~(G & C)        Premise

∴          T

(4)      U                                              5, &-Elimination

(5)      ~~U                                        4, DN

(6)      W → ~U                                  3, &-Elimination

(7)      ~W                                          5, 6 Modus Tollens

(8)      T v C                                        2, 7 Disjunctive Syllogism

(9)                  C                                  Assumption for RAA

(10)                U → G                          1, &-Elimination

(11)                G                                  4, 10 Modus Ponens

(12)                G & C                           9, 11 &-Introduction

(13)                ~(G & C)                     3 &-Elimination

(14)                (G&C) & ~(G&C)       12, 13 &-Introduction

(15)    ~C                                           9-14 RAA

(16)    T                                              8, 15 Disjunctive Syllogism