The Venn diagram representation x y x y z z x x y x - PDF document

Constant 1 Constant 0 x x x x (c) Variable x x x y x y + x . y x y x y x y z + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ x y z x y The Venn diagram representation

x y x y z z ⋅ ⋅ ⋅ ⋅ x x y x y x y z z + ⋅ ⋅ ⋅ ⋅ y z x z x y x y z z + + z ⋅ ⋅ ⋅ ⋅ ( ( ( ( ) ) ) ) ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ x y z x y x Verification of the distributive property

x y x y z z ⋅ ⋅ x y x y x y x y z z ⋅ ⋅ x z x z x y x y z z ⋅ ⋅ x y x z ⋅ + y z x y z ⋅ ⋅ ⋅ x y x z y z + + Verification of + + + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ x y x z y z = x y x z