Unit 6 Answers
1.
- Addition
- Simplification
- Modus ponens
- Modus tollens
- Disjunctive syllogism
2.
- The argument is translated as follows:
T S
T
C
S
----------------------------------------------------
C
The inference rules used are:
From
( T S )
  and S
by modus tollens we deduce
T
From
T and
( T
C )
by disjunctive syllogism we conclude C.
- The argument is translated as follows:
( S
W )  
 
( R
C )
-----------------------------------------------------
( W
C )
The inference rules used are:
( S
W )
is equivalent to
( S
W )
by implication and De Morgan
Also ( R
C )
is equivalent to
( R
C )
by De Morgan.
Hence
( S
W )
( R
C )
is equivalent to
( S
W )
( R
C ),
which is equivalent to
( S
R )
( W
C )
Hence by simplification
( W
C )
- The argument is translated as follows:
C S
O
L
O C
-----------------------------------------------------
S
L
The inference rules used are:
S
C
by Contrapositive of
C S
C
O
by Contrapositive of
O C
By hypothetical syllogism from the last two
S
O
By another hypothetical syllogism from this and
O
L,
S
L
is obtained.
- The argument is translated as follows:
G
F
Z M
M F
--------------------------------------------
Z G
The inference rules used are:
>From Z M
and
M F
by hypothetical syllogism
Z F
is obtained.
Then from G
F
by taking contrapositive M
F is obtained.
>From this and Z
F
by hypothetical syllogism
Z G
is obtained.
- The argument is translated as follows:
R
( H
L )
H
( L
R )
--------------------------------------------
R
The inference rules used are:
From H
( L
R ) by distributive law
( H
L )
( H
R )
From this by simplification
( H
L )
From this by De Morgan
( H
L )
With this and
R
( H
L )
by disjunctive syllogism R is concluded.