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LOGIC.TBL.CR
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1993-12-10
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61 lines
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LOGICAL EQUIVALENCE, NEGATION AND INVERSION
A TUTORIAL BY JAMES P. DAVIS
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"+" represents a "TRUE" or a "1" or an "ON" state in all cases.
"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
should be performed first. Nested parentheses, parentheses within
parentheses, means to perform the innermost operation first.
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BASIC LOGICAL TRUTH TABLE
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PROPOSITIONS = PREMISES CASE LOGICAL CONNECTIONS
------------------------------- ------------ -----------------------
1 2 3 4
------------------------------- ------------ -----------------------
Basic Premise: P + + o o P = not (not P)
Basic Premise: Q + o + o Q = not (not Q)
------------------------------- ------------ -----------------------
Basic Premise: not P o o + + not P = not (P)
Basic Premise: not Q o + o + not Q = not (Q)
------------------------------- ------------ -----------------------
A = P and Q + o o o A = not H = not S = Z
B = P and (not Q) o + o o B = not G = not T = Y
C = (not P) and Q o o + o C = not F = not U = X
D = (not P) and (not Q) o o o + D = not E = not V = W
------------------------------- ------------ -----------------------
E = P or Q + + + o E = not D = V = not W
F = P or (not Q) + + o + F = not C = U = not X
G = (not P) or Q + o + + G = not B = T = not Y
H = (not P) or (not Q) o + + + H = not A = S = not Z
------------------------------- ------------ -----------------------
S = not (P and Q) o + + + S = not A = H = not Z
T = not (P and (not Q)) + o + + T = not B = G = not Y
U = not ((not P) and Q) + + o + U = not C = F = not X
V = not ((not P) and (not Q)) + + + o V = not D = E = not W
------------------------------- ------------ -----------------------
W = not (P or Q) o o o + W = D = not E = not V
X = not (P or (not Q)) o o + o X = C = not F = not U
Y = not ((not P) or Q) o + o o Y = B = not G = not T
Z = not ((not P) or (not Q)) + o o o Z = A = not H = not S
------------------------------- ------------ -----------------------
Tautology: P or (not P) + + + + True in all cases.
Contradiction: P and (not P) o o o o False in all cases.
------------------------------- ------------ -----------------------
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