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BOOLEAN UNIT: BBCBASIC BOOLEAN CONCEPTSDeveloped by The Center for Conceptual StudiesPresented by: Richard Singer ccsfrs@worldnet.att.netPhone Number: (314) 721-2779Edition Date: 1/00This is the first in a collection of units on boolean algebra. Appendix 2 gives an outline describing these units and showing the relationship between them. Notation &: and : or : not: belongs to the setBoolean Lattice Laws This unit will introduce some specific structures called boolean lattices. The main laws that such structures satisfy are listed below for easy reference. You are notexpected to understand them until later.xy = yx xy = yxcommutative(xy)z = x(yz)(x+y)z = x+(yz)associative1x = xx1 = x0+x = xx+0 = xidentityx(yz) = (xy)(xz)x+(yz) = (x+y)(x+z)distributive0x = 0x0 = 01+x = 1x+1 = 1annihilatorx+(xy) = xx(x+y) = x absorptionxx = xx+x = xidempotentx/x = 0/xx = 0x+/x = 1/x+x = 1complement(xy)+(x/y) = x(x+y)(x+/y) = xreduction/(xy) = /x+/y/(x+y) = /x/y/(/x/y) = x+y /(/x+/y) = xy DeMorgan//x = xdouble complementBriefs Parentheses and multiplication signs may be omitted according to the usual conventions of ordinary algebra.Boolean Inequality: The relation is defined by: xy iff xy = xxx reflexive x

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