An Approach to Algebra
Claudia Patricia Chapa Tamez
Examples 1.5.1.3 Truth tables
Construct a truth table for each of the following compound propositions.
Note: all these examples can also be solved in an Excel spreadsheet by using the
corresponding Excel functions for the operators  (AND),(OR) and~ (NOT).
1)
 p  q  p
2)
 p  q  r
3)
 p   p  q  r
4)
 p  q  q  r 
5) ~ p  q
6) ~  p  q  ~ r
1
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An Approach to Algebra
Claudia Patricia Chapa Tamez
Solution
1)
 p  q  p
number of statements ( n )= 2
n
number of rows ( 2 )= 4
2)
p
T
T
F
F
 p  q  r
q
T
F
T
F
pq
 p  q  p
T
T
T
F
T
T
F
F
number of statements ( n )= 3
n
number of rows ( 2 )= 8
3)
p
T
T
T
T
F
F
F
F
 p   p  q  r
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
pq
 p  q  r
T
T
F
F
F
F
F
F
T
F
F
F
F
F
F
F
number of statements ( n )=3
n
number of rows ( 2 )= 8
p
T
T
T
T
F
F
F
F
2
q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
pq
 p   p  q
 p   p  q  r
T
T
T
T
T
T
F
F
T
T
T
T
T
T
F
F
T
F
T
F
T
F
F
F
D . R . © I n s t it u t o T e c n o l ó g i c o y d e E s t u d i o s Su p e r i o r e s d e M o n t e r r e y , M é x i co 2 0 12
An Approach to Algebra
Claudia Patricia Chapa Tamez
4)
 p  q  q  r 
number of statements ( n )= 3
n
number of rows ( 2 )= 8
p
T
T
T
T
F
F
F
F
Q
T
T
F
F
T
T
F
F
r
T
F
T
F
T
F
T
F
pq
qr
 p  q  q  r 
T
T
T
T
T
T
F
F
T
F
F
F
T
F
F
F
T
F
F
F
T
F
F
F
5) ~ p  q … be careful since the negation is only for p.
number of statements ( n )= 2
n
number of rows ( 2 )= 4
p
T
T
F
F
q
T
F
T
F
~p ~ p  q
F
T
F
F
T
T
T
T
6) ~  p  q  ~ r
number of statements ( n )= 3
n
number of rows ( 2 )= 8
p
T
T
T
T
F
F
F
F
3
q
T
T
F
F
T
T
F
F
R
T
F
T
F
T
F
T
F
~r
F
T
F
T
F
T
F
T
pq
T
T
F
F
F
F
F
F
~  p  q
F
F
T
T
T
T
T
T
~  p  q  ~ r
F
F
F
T
F
T
F
T
D . R . © I n s t it u t o T e c n o l ó g i c o y d e E s t u d i o s Su p e r i o r e s d e M o n t e r r e y , M é x i co 2 0 12