3 Statement _V_₁ to Dial Statements 1 to 12 or constant _V_₁₂ _T_ or _F_ 2 Statement ~ Snap Affirmative (down) or negative denial (up) 4 Connective _k_₁ to Dial ∧ (AND), _k_₁₁ ∨ (OR), ▲ (IF-THEN), ▼ (IF AND ONLY IF) 8 Connective ~ Snap Affirmative (down) or negative denial (up) 5 Antecedent _A_₁ to Dial _V_ or various _k_’s _A_₁₁ 6 Consequent _C_₁ to Dial _V_ or various _k_’s _C_₁₁ 7 Stop _S_₁ to Snap Not connected (down) or _S_₁₁ connected (up) The first step in putting a problem on the machine is to express the whole problem as a single compound statement that we want to know the truth or falsity of. We express the single compound statement in a form such as the following: _V k V k V k V k V k V k V k V k V k V k V k V_ where each _V_ represents a statement, each _k_ represents a connective, and we know the grouping, or in other words, we know the antecedent and consequent of each connective. For example, let us choose a problem with an obvious answer: PROBLEM. Given: statement 1 is true; and if statement 1 is true, then statement 2 is true; and if statement 2 is true, then statement 3 is true; and if statement 3 is true, then statement 4 is true. Is statement 4 true? How do we express this whole problem in a form that will go on the machine? We express the whole problem as a single compound statement that we want to know the truth or falsity of: If [1 and (if 1 then 2) and (if 2 then 3) and (if 3 then 4)], then 4 The 8 statements occurring in this problem are, respectively: 1 1 2 2 3 3 4 4. These are the values at which the _V_ switches (the statement dial switches, Unit 2) from _V_₁ to _V_₈ are set. The 7 connectives occurring in this problem are, respectively: AND, IF-THEN, AND, IF-THEN, AND, IF-THEN, IF-THEN. These are the values at which the _k_ switches (the connective dial switches, Unit 4) from _k_₁ to _k_₇ are set. A grouping (one of several possible groupings) that specifies the antecedent and consequent of each connective is the following: