Boolean Algebra

George Boole [2/11/ 1815 – 8/12/ 1864]: 《The Laws of Thought》: symbolic logic representation of thought.

Let x = class of sheep’s

y = white

=> white sheep = xy = yx = sheep white

then Commutativity Law:

\boxed {xy = yx}

Let x= rivers, y = estuaries河口, z= navigable 通航

then, Associativity Law:

\boxed {(xy)z= x(yz)}

A sheep is a sheep,

\boxed {xx = x^{2} = x}

Note: x = 0 or 1 fulfills the above equation.

If x = class of men

y = class of women

z = class of adults (either men or women)

\boxed {z = x + y}

w = European

then Distributive Law:

\boxed {w(x+y) = wx + wy}

If t = Chinese

then all non-Chinese men = {x – t}

If s = Singaporean,


\boxed {s(x - t ) = sx - st}


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