rules-if-inference

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
⊃
Q
2. (R
•
S)
⊃
P
3. R
:
.
S
⊃
Q
4. (R
•
S)
⊃
Q
5. ∼(R
•
S)
∨
Q
6. (∼R
∨
∼S)
∨
Q
7. ∼R
∨
(∼S
∨
Q)
8. R
⊃
(∼S
∨
Q)
9. (∼S
∨
Q)
10. S
⊃
Q
Argument
2
1. T
∨
S
2. ∼T
3. (S
∨
S)
⊃
(∼P
∨
R)
:
.
∼R
⊃
∼P
4. S
5. S
∨
S
6. ∼P
∨
R
7. R
∨
∼P
8. ∼R
⊃
∼P
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. ∼P
2. ∼Q
⊃
P
3. ∼Q
∨
(∼P
⊃
R)
:
.
R
∨
S
4.
2,
1
MT
5.
3
Impl
6.
5,
4
MP
7.
6,
1
MP
8.
7
Add
Argument
2
1. P
⊃
(∼Q
•
R)
2. R
⊃
Q
:
.
∼P
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. ∼P
2. (Q
∨
P)
∨
R
:
.
Q
∨
R
Argument
2
1. ∼(P
•
P)
:
.
P
⊃