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Download Principles of the Algebra of Logic, with Examples by Alexander MacFarlane PDF

By Alexander MacFarlane

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Extra resources for Principles of the Algebra of Logic, with Examples

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For example ; if If II. other 41 Inference. ; x=y, and a=b; x a=y b. then III. If two equations be multiplied together ing equation ; the result is true. x=y, and #==$/ then ax=by. IV. If two equations be divided the one by the other the resulting equation is true. x=y, and ; a=b ; ^ = Z. then a b not necessary, that the two equations should contain a common character ; but it is necessary that both should refer to the same universe just as the ordinary 116. It is : a given investigation must be sup posed to refer to the same unit.

That the Universe contains a great number of cubes, in order that each portion of the y line may be supposed to be straight. 63. Venn shows Logic of Chance, rule the true nature of the assumption in his For the establishment of the 157 p. under discussion, : both necessary and sufficient by each of the above should each sub-divide of the classes created distinctions, by the other distinction in the same ratio in which it sub divides the whole. If the independence be granted and so it is that the division into classes caused The Signs x and 22 defined as to mean this, -r- the rule of course will stand, but, without especial attention being drawn to the point, it does not seem that the word would naturally be so understood.

X=y; z=z, If an equation and an identical equation be sub- The Principle of Identity and 38 tracted the one from the other ; the resulting equation is true. Thus x-y\ if since z=z, xz=yz. If an equation III. tiplied together Thus ; and an identical equation be the resulting equation mul is true. x=y if since z=z, xz=yz. IV. If an equation and an identical equation be divided the one by the other ; the resulting equation is true. Thus x=y; z=z if since A common form of application of Axiom II. 109.

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