# Download The Mathematical Analysis of Logic by George Boole PDF

By George Boole

George Boole was once an English mathematician and philosopher. He labored within the fields of differential equations and algebraic common sense. Boolean common sense (once defined as "0 and 1" good judgment) is credited with laying the principles for the knowledge age. In 1841 Boole released an influential paper in early invariant concept. He acquired a medal from the Royal Society for his 1844 paintings, On A normal approach to research. It was once a contribution to the speculation of linear differential equations, relocating from the case of continuous coefficients on which he had already released, to variable coefficients. In 1847 Boole released The Mathematical research of good judgment, the 1st of his works on symbolic common sense.

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**Example text**

Is gives which implies that - /. 1, is i (39), 9 In like manner true. with the assumptions that and the equation 0, Y is true, or that x = Again, in virtue of the property the equation in the form x 1 - Ixy + y* = Y x, y* = we may proceed is false. y, we may write 1, and extracting the square root, we have x - y = 1, (40), and or this as when represents the actual case; for, is respectively false or true, we have X is true false, Y x = /. There will be no y = x - y 1 or 0, or = 1 1, or - 1. of other cases.

X express the disjunctive Proposition, Either Z is true, the members being exclusive. is true, or true, or E 2 OF HYPOTHETIC A LS. Here the mutually exclusive cases are 1st, X true, Y false, Z 2nd, Y 3rd, Z X false, Y false, Z true, false, X false, true, and the sum of the x(\ - y) false, y (1 - (1 z) (1 - 2), x), * (1 - a) (1 - y), elective expressions equated to 1, gives, upon reduction, x + y + - 2 (xy + yz + zz) 4 Say* = z The of the same Proposition, expression are in no sense exclusive, will be - (1 And it - x) (1 - y) (1 = z) 0, 1, (34).

1 x) o = Zy /. The implied, y) considered as repre = v c are not Xs. (1 - Some not-Xs x) z are not Zs. premiss here permits us to interpret does not enable us to interpret vz. first- D2 38 OF SYLLOGISMS. Of which no inference in cases is possible, we take as examples AO, 1, Fig. and, by mutation, AllYsareXs, Some Zs are not Ys, OA, Fig. 4, y(\-x)=Q 2/(l-z)=0, vz - v (1 - y) v(l -z) = vy (a) i>(l-*)(l-aO-0 ) = since the auxiliary equation in this case it is satisfactory to vz as Some do Zs, but it so.