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Philosophy 103: Introduction to LogicHow to Construct a Truth Table
Abstract: The general principles for the construction of truth tables are explained and illustrated.
- How to construct the guide columns:
- Write out the number of variables (corresponding to the number
of statements) in alphabetical order.
- The number of lines needed is 2n where n is the number
of variables. (E. g., with three variables, 23 = 8).
- Start in the right-hand column and alternate T's
and F's until you run out of lines.
- Then move left to the next column and alternate pairs of
T's and F's until you run out of lines.
- Then continue to the next left-hand column and double the
numbers of T's and F's until completed.
- Write out the number of variables (corresponding to the number
of statements) in alphabetical order.
- Example: construct a truth table for p
( q r )
Line
No.
↓I, A variables in alphabetical
order
↓III, A
First
line
all T
→
p q r q rp
(q r)1 T T T T T I, B
number of lines
= 2n
→
III, D
half T's
half F's2 T T F T T 3 T F T T T 4 T F F F T 5 F T T T T 6 F T F T T 7 F F T T T 8 F F F F F III, B
last
line
all F
↑
I, E
alternate
double of previous
T and F↑
I, D
alternate
pairs of
T and F
↑
I, C
alternate
T and F
- As check that the guide columns were done correctly:
- The first horizonal line will be all T's.
- The last horizonal line will be all F's.
- The left-most column will be evenly divided; the first half all T's and the second half all F's.
- The first horizonal line will be all T's.
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12.26.04
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