Part
1
Complete
the
logical
proof
for
each
of
the
following
arguments
using
the
18
rules
of
inference.
Provide
the
justification
(line
numbers
needed
for
the
derivation
and
rule
of
inference)
for
each
step
of
the
proof.
Argument
1
1. P
âŠƒ
Q
2. (R
â€¢
S)
âŠƒ
P
3. R
:
.
S
âŠƒ
Q
4. (R
â€¢
S)
âŠƒ
Q
5. âˆ¼(R
â€¢
S)
âˆ¨
Q
6. (âˆ¼R
âˆ¨
âˆ¼S)
âˆ¨
Q
7. âˆ¼R
âˆ¨
(âˆ¼S
âˆ¨
Q)
8. R
âŠƒ
(âˆ¼S
âˆ¨
Q)
9. (âˆ¼S
âˆ¨
Q)
10. S
âŠƒ
Q
Argument
2
1. T
âˆ¨
S
2. âˆ¼T
3. (S
âˆ¨
S)
âŠƒ
(âˆ¼P
âˆ¨
R)
:
.
âˆ¼R
âŠƒ
âˆ¼P
4. S
5. S
âˆ¨
S
6. âˆ¼P
âˆ¨
R
7. R
âˆ¨
âˆ¼P
8. âˆ¼R
âŠƒ
âˆ¼P
Chapter
8:
Logical
Proofs
Homework
Part
2
Complete
the
logical
proof
for
each
of
the
following
arguments
using
the
18
rules
of
inference.
Provide
the
derivation
for
each
step
of
the
proof
given
its
justification
(line
numbers
needed
for
the
derivation
and
rule
of
inference).
Argument
1
1. âˆ¼P
2. âˆ¼Q
âŠƒ
P
3. âˆ¼Q
âˆ¨
(âˆ¼P
âŠƒ
R)
:
.
R
âˆ¨
S
4.
2,
1
MT
5.
3
Impl
6.
5,
4
MP
7.
6,
1
MP
8.
7
Add
Argument
2
1. P
âŠƒ
(âˆ¼Q
â€¢
R)
2. R
âŠƒ
Q
:
.
âˆ¼P
3.
2
Impl
4.
3
DM
5.
4
Com
6.
1,5
MT
Chapter
8:
Logical
Proofs
Homework
Part
3
Construct
a
logical
proof
for
each
of
the
following
arguments
using
the
18
rules
of
inference.
Provide
the
derivation
for
each
step
of
the
proof
given
its
justification
(line
numbers
needed
for
the
derivation
and
rule
of
inference).
Argument
1
1. âˆ¼P
2. (Q
âˆ¨
P)
âˆ¨
R
:
.
Q
âˆ¨
R
Argument
2
1. âˆ¼(P
â€¢
P)
:
.
P
âŠƒ