Proposition 1 . 1 . 3 : Distributive Law for Sets ProofDiagram, VennHence, C
distributive law of dot product over additionTheorem 1.5, part (2), and x ⋅ y = ||x|| ||y||because c=‖y‖‖x‖,which equals zero, and so w = 0. The proof is complete. Note that two proofs are required to prove an “if and only if” type of statement — one for each...
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1.3TechniquesofProof:I inductivereasoning counterexample deductivereasoning hypothesis conclusion contrapositive 1 2CHAPTER1.LOGICANDPROOF converse inverse contradiction 1.4TechniquesofProof:II Chapter2 SetsandFunctions 2.1BasicSetOperations elementsormembersofaset ...
It was soon realized that the distributive law was a defining property for lattices of sets (although Peirce seems to have thought it followed from the lattice axioms). Word problems for these lattices could be solved; whether by using conjunctive and disjunctive normal forms, by truth tables, ...
Proof of Riemann hypothesis and the distributive law of odd primes in natural numbersZhang Xi-wen