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\$2S0S1S2S3S4S5S6S7S8S9S10S11S12S13S14S15
C0TTFFFFFFFFTTTTTTTT
C1TFFFFFTTTTFFFFTTTT
C2FTFFTTFFTTFFTTFFTT
C3FFFTFTFTFTFTFTFTFT

`  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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