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Section 1.2
11. [BB] The third and sixth
columns of the truth table show
that
(p
t
q)
'¢=}
((,q)
t
(,p)).
12. The third and sixth
columns of the truth table
show that
(p
~
q)
'¢=}
((p
t
q)
/\
(q
t
p)).
13. [BB] The third and fifth columns
0
the truth table show that
(p
t
q)
'¢=}
((,p)
V
q).
2. (a) We construct a truth table.
Since
p
V
[,(p
/\
q)]
is true
for all values of
p
and
q,
this statement is a
tautology.
p
q
T
T
T
F
F
T
F
F
f
p
T
T
F
F
17
p
q
p+q 'q 'p (,q)
+
(,p)
T
T
T
F
F
T
T
F
F
T
F
F
F
T
T
F
T
T
F
F
T
T
T
T
p .
.... q
p+q q+p (p
+
q) 1\ (q
+
p)
T
T
T
T
F
F
T
F
F
T
F
F
T
T
T
T
p
q
p+q ,p (,p)
V
q
T
T
T
F
T
T
F
F
F
F
F
T
T
T
T
F
F
T
T
T
q
p/\q ,(p
/\
q)
P
V
[,(p
/\
q)]
T
T
F
T
F
F
T
T
T
F
T
T
F
F
T
T
(b) By one of the laws of DeMorgan, the negation is
(,p)
/\
(p
/\
q).
By associativity, this is logically
equivalent to [(
,p)
/\
p]/\ q
'¢=}
0 /\
q
'¢=}
O. So the negation is a contradiction.
3. (a) [BB] Using one of the laws of De Morgan and one distributive property, we obtain
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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