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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