Built-in Mathematica Symbol

Boole

Boole[expr]
yields 1 if expr is True and 0 if it is False.

Integrate[f Boole[pred], ...] can be used to integrate f over the region in which pred is True.

Convert a list of truth values to integers:

Find the area of the disc defined by the inequality

:

Convert a list of truth values to integers:

Find the area of the disc defined by the inequality

:

Find the area of a region defined by an inequality:

Plot the region:

Find the volume of a solid defined by an inequality:

Plot the solid:

Find the area of the intersection of a circle with a parametric radius and a square:

Convert a table of True, False values to 1, 0 for plotting:

The inverse of Boole:

Correspondence between logic operations on conditions and arithmetic operations on Boole:

Use Refine, Simplify and FullSimplify to transform expressions involving Boole:

Reduce equations and optimize functions involving Boole:

Use Boole as a characteristic function for integration problems: