To understand this project see project: Boolean Algebra and Claude Shannon Part 1 https://scratch.mit.edu/projects/707370215/ Axiom 1b. x⊗y=y⊗x (commutative property) Press the Green Flag and verify that the x, y, inputs generate the two columns on the right side of the table.
A Boolean Algebra is a set B on which are defined two binary operations ⊕ and ⊗ and one unary operation ' and in which there are two distinct elements O and I such that the following properties hold for all x, y, z that are elements of B. Undefined elements: x, y, z, etc. The elements O and I are special elements whose properties are specified in the axioms. Undefined operations: ⊕, ⊗, ' Axioms: Commutative Properties 1a. x⊕y=y⊕x 1b.x⊗y=y⊗x Associative Properties 2a. (x⊕y)⊕z=x⊕(y⊕ z) 2b.(x⊗y)⊗ z=x⊗(y⊗z) Distributive Properties 3a. x⊕ (y⊕ z)=(x⊕ y)⊕ (x⊕ z) 3b.x⊗ (y⊗ z)=(x⊗ y)⊗ (x⊗ z) Identity Properties 4a. x⊕ O=x 4b.x⊗I=x Inverse Properties 5a. x⊕x'=I 5b.x⊗ x'=O Idempotent Laws 6a. x ⊕ x = x 6b. x ⊗ x = x
