The Calculus of Logic by George Boole, is part of the HackerNoon Books Series. You can jump to any chapter in this book . Theorems of Development. here Theorems of Development. (1) If be any elective symbol, then x (2) For a function of two elective symbols we have (3) Functions of three symbols, From these examples the general law of development is obvious. And I desire it to be noted that this law is a mere consequence of the primary laws which have been expressed in (1), (2), (3). This enables us to interpret any equation by a general rule. RULE. 0 Bring all the terms to the first side, expand this in terms of all the elective symbols involved in it, and equate to every constituent whose modulus does not vanish. For the demonstration of these and many other results, I must refer to the original work. It must be noted that on p. 66[4], has been, through mistake, substituted for and that the reference on p. 80[5] should be to Prop. 2. z w, As an example, let us take the equation the former implies that there are no Xs which are not-Ys, the latter that there are no Ys which are not-Xs, these together expressing the full significance of the original equation. We can, however, often recombine the constituents with a gain of simplicity. In the present instance, subtracting (12) from (11b), we have or All equations are thus of equal significance which give, on expansion, the same series of constituent equations, and . all are interpretable [4] The Mathematical Analysis of Logic [5] Ibid. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. George Boole (2022). The calculus of logic. Urbana, Illinois: Project Gutenberg. Retrieved October 2022 https://www.gutenberg.org/cache/epub/69512/pg69512-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

Theorems of Development.

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