The book Principles of the Algebra of Logic With Examples was written by author Alexander Macfarlan Here you can read free online of Principles of the Algebra of Logic With Examples book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Principles of the Algebra of Logic With Examples a good or bad book?
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X=y+w, x>y, and xy=y, express the same truth. To express the truth considered by means of an equation, either three symbols must be used, or else a term of the second order introduced. 250. Inference from two disjunctive equations having a common character. First; when the character occurs oppositely in the two equations. x=y+z. (i) x'=i-y+z'. (2) Add; x+x'=i+z+z', that is, x i x' +z+z'. Second; when the character occurs similarly in the two equations. x=y+z. (i) x'=y+z f . (2) Subtract ; x x' ...= z z', that is, x=x'+z z r . 1 10 On certain forms of the Observation. When z and z' are each indefinite, the former conclusion amounts to Only 7's which are x are not x'. The latter conclusion under the same conditions amounts to Some 7's which are x are x. For x>z, by equation (i). 251. If x=x(y+z), then x=x{y(i z)+z(i y)}- } and conversely. that is, x{i+y-\-z 2y2z -\-2yz} =*>, that is, x{i-y(i-z)-z(i-y)}=o, that is, x=x{y(i z)+z(i y)}. As this proof can be reversed, the converse proposition must be true.
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