Boole's expansion theorem
THEOREM IN BOOLEAN ALGEBRA
Shannon's expansion theorem; Shannon cofactor; Shannon's Expansion Theorem; Shannon expansion; Shannon decomposition; Shannon's expansion; Fundamental theorem of Boolean algebra; Boole's expansion; Boole expansion; Boole–Shannon expansion; Boole-Shannon expansion
Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: F = x \cdot F_x + x' \cdot F_{x'}, where F is any Boolean function, x is a variable, x' is the complement of x, and F_xand F_{x'} are F with the argument x set equal to 1 and to 0 respectively.