This preview shows page 1. Sign up to view the full content.
Section 1.3
which we check with a truth table.
p
q
8
T
T
T
T
F
T
F
T
T
F
F
T
T
T
F
T
F
F
F
T
F
F
F
F
pVq p'>8
T
T
T
T
T
T
F
T
T
F
T
F
T
T
F
T
qV8
T
T
T
T
T
F
T
F
*
*
*
*
23
There are four rows when the premises are true and, in each case, the conclusion is also true. The
argument is valid.
(d) Since
«
,q)
"
r)
¢:::=}
,
(q
V
(,r))
and ,
(p
"
8)
¢:::=}
[(
,p)
V ('8)]
¢:::=}
(p
'>
('8)), the
premises become
(q
V
(,r))
'>
p
P
'>
('8)
so the chain rule gives
(q
V
(,r))
'>
('8), which is logically equivalent to (,(
q
V
(,r)))
V ('8),
which is the desired conclusion by a law of De Morgan.
4. (a) [BB] Since
[(,r)
V
(,q)]
¢:::=}
[q
'>
(,r)],
the first two premises give
p
'>
(,r)
by the chain
rule. Now
,p
follows by modus tollens.
(b) This argument is not valid.
If
q
and
r
are false,
p
and
8
are true, and
t
takes on any truth value,
then all premises are true, yet the conclusion is false.
This is the end of the preview. Sign up
to
access the rest of the document.
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

Click to edit the document details