1 AND 1 IF-THEN 2 AND 2 IF-THEN 3 AND 3 IF-THEN 4 IF-THEN 4 | | | | | | +—————————+ +—————————+ +—————————+ _k_₂ _k_₄ _k_₆ | | | | +———————————————+ +—————————————————————————+ _k_₁ _k_₅ | | +———————————————————————————————————————————————+ _k_₃ | | +—————————————————————————————————————————————————————————+ _k_₇ 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. Table 13 ANTECEDENT CONSEQUENT CONNECTIVE SWITCH SET AT SWITCH SET AT _k_₁ _A_₁ _V_ _C_₁ _k_₂ _k_₂ _A_₂ _V_ _C_₂ _V_ _k_₃ _A_₃ _k_₁ _C_₃ _k_₅ _k_₄ _A_₄ _V_ _C_₄ _V_ _k_₅ _A_₅ _k_₄ _C_₅ _k_₆ _k_₆ _A_₆ _V_ _C_₆ _V_ _k_₇ _A_₇ _k_₃ _C_₇ _V_ In any problem, statements that are different are numbered one after another 1, 2, 3, 4 ···. A statement that is repeated bears always the same number. In nearly all cases that are interesting, there will be repetitions of the statements. If any statement appeared with a “NOT” in it, we would turn up the denial switch for that statement (Unit 2). The different connectives available on the machine are “AND,” “OR,” “IF ··· THEN,” “IF AND ONLY IF.” If a “NOT” affected the compound statement produced by any connective, we would turn up the denial switch for that connective (Unit 8). The last step in putting the problem on the machine is to connect the main connective of the whole compound statement to the yellow light output (Unit 12). In this problem the last “IF-THEN,” _k_₇, is the main connective, the one that produces the whole compound statement. So we turn Stop Switch 7 (in Unit 7) that belongs to _k_₇ into the up position. There are a few more things to do, naturally, but the essential part of putting the information of the problem into the machine has now been described. HOW INFORMATION COMES OUT OF THE MACHINE Of the 16 units listed in Table 11, 3 are output units, and only 2 of these are really important, as shown in Table 14. Table 14