# propositions.operators module¶

Syntactic conversion of propositional formulas to use only specific sets of operators.

`propositions.operators.``to_not_and_or`(formula)

Syntactically converts the given formula to an equivalent formula that contains no constants or operators beyond `'~'`, `'&'`, and `'|'`.

Parameters

formula (`Formula`) – formula to convert.

Return type

`Formula`

Returns

A formula that has the same truth table as the given formula, but contains no constants or operators beyond `'~'`, `'&'`, and `'|'`.

`propositions.operators.``to_not_and`(formula)

Syntactically converts the given formula to an equivalent formula that contains no constants or operators beyond `'~'` and `'&'`.

Parameters

formula (`Formula`) – formula to convert.

Return type

`Formula`

Returns

A formula that has the same truth table as the given formula, but contains no constants or operators beyond `'~'` and `'&'`.

`propositions.operators.``to_nand`(formula)

Syntactically converts the given formula to an equivalent formula that contains no constants or operators beyond `'-&'`.

Parameters

formula (`Formula`) – formula to convert.

Return type

`Formula`

Returns

A formula that has the same truth table as the given formula, but contains no constants or operators beyond `'-&'`.

`propositions.operators.``to_implies_not`(formula)

Syntactically converts the given formula to an equivalent formula that contains no constants or operators beyond `'->'` and `'~'`.

Parameters

formula (`Formula`) – formula to convert.

Return type

`Formula`

Returns

A formula that has the same truth table as the given formula, but contains no constants or operators beyond `'->'` and `'~'`.

`propositions.operators.``to_implies_false`(formula)

Syntactically converts the given formula to an equivalent formula that contains no constants or operators beyond `'->'` and `'F'`.

Parameters

formula (`Formula`) – formula to convert.

Return type

`Formula`

Returns

A formula that has the same truth table as the given formula, but contains no constants or operators beyond `'->'` and `'F'`.