Table 12
| Unit | Name of Switches | Mark | Kind of Switch | Switch Settings |
|---|---|---|---|---|
| 3 | Statement | V₁ to V₁₂ | Dial | Statements 1 to 12 or constant T or F |
| 2 | Statement denial | ~ | Snap | Affirmative (down) or negative (up) |
| 4 | Connective | k₁ to k₁₁ | Dial | ∧ (and), ∨ (or), ▲ (if-then), ▼ (if and only if) |
| 8 | Connective denial | ~ | Snap | Affirmative (down) or negative (up) |
| 5 | Antecedent | A₁ to A₁₁ | Dial | V or various k’s |
| 6 | Consequent | C₁ to C₁₁ | Dial | V or various k’s |
| 7 | Stop | S₁ to S₁₁ | Snap | Not connected (down) or 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 V₁ to V₈ 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 k₁ to k₇ are set.
A grouping (one of several possible groupings) that specifies the antecedent and consequent of each connective is the following:
| 1 | and | 1 | if-then | 2 | and | 2 | if-then | 3 | and | 3 | if-then | 4 | if-then | 4 |
| | | | | | | | | | | | | |||||||||
| k₂ | k₄ | k₆ | ||||||||||||
| | | | | | | | | |||||||||||
| k₁ | k₅ | |||||||||||||
| | | | | |||||||||||||
| k₃ | ||||||||||||||
| | | | | |||||||||||||
| k₇ | ||||||||||||||
The grouping has here been expressed graphically with lines but may be expressed in the normal mathematical way with parentheses and brackets as follows:
{[ 1 and (1 if-then 2)] and [(2 if-then 3) and (3 if-then 4) ] } if-then 4.
So the values at which the antecedent and consequent dial switches are set are as shown in Table 13.