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LOGIC.TABLE
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.txt
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AppleWorks Document
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1993-12-10
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4KB
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54 lines
O===============================================================================
O=====<====<====<====<====<====<====<====<====<====<====<====<====<====<====<===
------------------------------ ------------ -------
O=====<====<====<====<====<====<====<====<====<====<====<====<====<====<====<===
----------------------------------------------------------------------
LOGICAL EQUIVALENCE, NEGATION AND INVERSION
A TUTORIAL BY JAMES P. DAVIS
----------------------------------------------------------------------
"+" represents a "TRUE" or a "1" or an "ON" state in all cases.D
"o" represents a "FALSE" or a "0" or an "OFF" state in all cases.
"=" represents equivalence: two things being equal to each other.
"not" means to negate or change to the opposite state.
? Parentheses, "(" & ")", are used for grouping operations that E
Cshould
be performed first. Nested parentheses, parentheses within >
parentheses, means to perform the innermost operation first.
----------------------------------------------------------------------
BASIC LOGICAL TRUTH TABLE
----------------------------------------------------------------------F
PROPOSITIONS = PREMISES CASE LOGICAL CONNECTIONSH
------------------------------- ------------ -----------------------.
1 2 3 4H
------------------------------- ------------ -----------------------A
Basic Premise: P + + o o P = not (not P)A
Basic Premise: Q + o + o Q = not (not Q)H
------------------------------- ------------ -----------------------A
Basic Premise: not P o o + + not P = not (P)A
Basic Premise: not Q o + o + not Q = not (Q)H
------------------------------- ------------ -----------------------G
A = P and Q + o o o A = not H = not S = ZG
B = P and (not Q) o + o o B = not G = not T = YG
C = (not P) and Q o o + o C = not F = not U = XG
D = (not P) and (not Q) o o o + D = not E = not V = WH
------------------------------- ------------ -----------------------G
E = P or Q + + + o E = not D = V = not WG
F = P or (not Q) + + o + F = not C = U = not XG
G = (not P) or Q + o + + G = not B = T = not YG
H = (not P) or (not Q) o + + + H = not A = S = not ZH
------------------------------- ------------ -----------------------G
S = not (P and Q) o + + + S = not A = H = not ZG
T = not (P and (not Q)) + o + + T = not B = G = not YG
U = not ((not P) and Q) + + o + U = not C = F = not XG
V = not ((not P) and (not Q)) + + + o V = not D = E = not WH
------------------------------- ------------ -----------------------G
W = not (P or Q) o o o + W = D = not E = not VG
X = not (P or (not Q)) o o + o X = C = not F = not UG
Y = not ((not P) or Q) o + o o Y = B = not G = not TG
Z = not ((not P) or (not Q)) + o o o Z = A = not H = not SH
------------------------------- ------------ -----------------------D
Tautology: P or (not P) + + + + True in all cases.E
Contradiction: P and (not P) o o o o False in all cases.H
------------------------------- ------------ -----------------------H
----------------------------------------------------------------------