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:

$latex boxed {xy = yx}&fg=aa0000&s=3 $

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

then, AssociativityLaw:

$latex boxed {(xy)z= x(yz)}&fg=aa0000&s=3 $

A sheep is a sheep,

$latex boxed {xx = x^{2} = x}&fg=aa0000&s=3 $

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)

$latex boxed {z = x + y}&fg=aa0000&s=3 $

w = European

then Distributive Law:

$latex boxed {w(x+y) = wx + wy}&fg=aa0000&s=3 $

If t = Chinese

then all non-Chinese men = {x – t}

If s = Singaporean,

then

$latex boxed {s(x – t…