This table shows the patterns of combination and selection of propositional logic with \ and | replaced with T and F. Then we give the familiar logical names of S0 to S15.
| $1 | $2 | S0 | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 | S13 | S14 | S15 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| C0 | T | T | → | F | F | F | F | F | F | F | F | T | T | T | T | T | T | T | T |
| C1 | T | F | → | F | F | F | F | T | T | T | T | F | F | F | F | T | T | T | T |
| C2 | F | T | → | F | F | T | T | F | F | T | T | F | F | T | T | F | F | T | T |
| C3 | F | F | → | F | T | F | T | F | T | F | T | F | T | F | T | F | T | F | T |
S0 F
S1 (NOT (OR $1 $2))
S2 (NOT (IMPLIES $2 $1)) ; note reversal of input arguments
S3 (NOT $1)
S4 (NOT (IMPLIES $1 $2))
S5 (NOT $2)
S6 (NOT (EQUIVALENT $1 $2))
S7 (NOT (AND $1 $2))
S8 (AND $1 $2)
S9 (EQUIVALENT $1 $2)
S10 $2
S11 (IMPLIES $1 $2)
S12 $1
S13 (IMPLIES $2 $1) ; note reversal of input arguments
S14 (OR $1 $2)
S15 T
(IMPLIES $1 $2) → (OR (NOT $1) $2)
(EQUIVALENT $1 $2) → (OR (AND $1 $2) (AND (NOT $1) (NOT $2)))
If you want to get rid of OR:
(OR $1 $2) → (NOT (AND (NOT $1) (NOT $2)))
If you want to get rid of AND:
(AND $1 $2) → (NOT (OR (NOT $1) (NOT $2)))
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