A Symbolic Analysis of Relay and Switching Circuits

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7
except for an illu str~tive example. Tbe method of
Proof is that of' "perfect induction," i.e., the verification
of the theorem for all possi ble cases.
Since
~r Pos~llpte 4 each variable is limited to the values
o Bn d 1, this is B simple rna tter. Some of the the orems
may be Droved more elegantly by recourse to p~evious
theorems, Cut the method of perfect induction is so univer·sal
thatit is pro ba bly to be preferred.
1. 8. X + Y • y + x
b. xy =yx
2. a. x + (y + &) = (x + y) + g
b. X(YIi) ..
(xy)&
-
3. a • x(y + ii) ..
xy + X5
b. x + yfll
-
(x + y) (x + a-)
-
4. a • l-x ..
x
-
b. 0 + x x
5. a • 1 + x • 1
b. O·x = 0
For example, to Drove theo rem 4A,
X is either ° or 1.
..
note the t
If it is 0, the theorem f'ollows
from 1)ostll1ate 2b; if 1, it folLOWS from rOs'tulate 3b.
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'Je
shall now define a new ope!'ation to be
oalled negstion. rhe negative of a ~inderance X Will
be Written X t and is defined as a variable Which is
equal to 1 When X equals 0 and equal to 0 When X
I