3-CNF equivalences for simple Boolean expressions.

We may use clauses of length 1 or 2, with the understanding that
terms will be duplicated as needed so that every clause has 3 terms.

a             (a)
!a            (!a)
a==b          (a||!b)&&(!a||b)
a=!b, a!=b    (a||b)&&(!a||!b)
a&&b          (a)&&(b)
a||b          (a||b)
a<=b          (!a||b)
a==(b&&c)     (!a||b)&&(!a||c)&&(a||!b||!c)
a==(b||c)     (a||!b)&&(a||!c)&&(!a||b||c)
a==(b<=c)     (a||b)&&(a||!c)&&(!a||!b||c)
a==(b==c)     (a||b||c)&&(a||!b||!c)&&(!a||b|||!c)&&(!a||!b||c)

In-class notation is not the same as C++ notation.  We will use "+"
to denote "or," while "and" will be denoted by simple justaposition
if it's unambiguous, otherwise by a "*".  We will also use a double
right arrow to denote "implies."

Here is the above table using the notation we will use in class:

a             (a)
!a            (!a)
a=b           (a+!b)(!a+b)
a=!b, !(a=b)  (a+b)(!a+!b)
a*b           (a)(b)
a+b           (a+b)
a=>b          (!a+b)
a=(b*c)       (!a+b)(!a+c)(a+!b+!c)
a=(b+c)       (a+!b)(a+!c)(!a+b+c)
a=(b=>c)      (a+b)(a+!c)(!a+!b+c)
a=(b=c)       (a+b+c)(a+!b+!c)(!a+b+!c)(!a+!b+c)