Count the number of cases for which yields true:

This corresponds to the number of times True appears in the truth table:

Count the number of truth cases for a pure Boolean function:

The corresponding table:

Count the truth instances in an expression with 2000 variables:

SatisfiabilityCount for a function of variables is always between and :

SatisfiabilityCount efficiently counts the number of True elements in BooleanTable:

In this case, the BooleanTable would have elements:

SatisfiableQ efficiently tests whether SatisfiabilityCount is greater than zero:

TautologyQ efficiently tests whether SatisfiabilityCount is for an n variable function:

The SatisfiabilityCount for primitives of n variables is simple; for And it is always :

For Or it is :

For Nand it is :

For Nor it is :

For Xor it is :

For Xnor it is :

For Equivalent it is :

For Majority it is for odd and for even :

The size of the truth set for BooleanCountingFunction is the length of Subsets:

The size of the truth set for BooleanCountingFunction can be given by a combinatorial sum:

SatisfiabilityCount for an indexed BooleanFunction is given by DigitCount:

For n variables the number is given by DigitCount of Mod[k,2^2^n]:

SatisfiabilityCount for BooleanMinterms is given by the length of the index list:

For BooleanMaxterms it is given by 2ⁿ minus the length of the index list:

Use SatisfiabilityInstances to find explicit instances:

Get three instances:

Use CountRoots to count the number of polynomial roots in a real interval:

Or a complex rectangle:

Count the number of truth instances for all Boolean functions of two variables:

Three variables:

Four variables: