Answer to exercise #1e


Step 1

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
T
T
T
T
T T T F
F
T
T
T
T T F T
T
T
T
F
T T F F
F
T
T
F
T F T T
T
T
F
T
T F T F
F
T
F
T
T F F T
T
T
F
F
T F F F
F
T
F
F
F T T T
T
F
T
T
F T T F
F
F
T
T
F T F T
T
F
T
F
F T F F
F
F
T
F
F F T T
T
F
F
T
F F T F
F
F
F
T
F F F T
T
F
F
F
F F F F
F
F
F
F

Step 2

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
T
T
T
T
T
T T T F
F
T
T
T
T
T T F T
T
T
T
T
F
T T F F
F
T
T
T
F
T F T T
T
T
F
F
T
T F T F
F
T
F
F
T
T F F T
T
T
F
F
F
T F F F
F
T
F
F
F
F T T T
T
F
F
T
T
F T T F
F
F
F
T
T
F T F T
T
F
F
T
F
F T F F
F
F
F
T
F
F F T T
T
F
F
F
T
F F T F
F
F
F
F
T
F F F T
T
F
F
F
F
F F F F
F
F
F
F
F

Step 3

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
T
F
T
T
T
T
T T T F
F
F
T
T
T
T
T T F T
T
F
T
T
T
F
T T F F
F
F
T
T
T
F
T F T T
T
T
T
F
F
T
T F T F
F
T
T
F
F
T
T F F T
T
T
T
F
F
F
T F F F
F
T
T
F
F
F
F T T T
T
T
F
F
T
T
F T T F
F
T
F
F
T
T
F T F T
T
T
F
F
T
F
F T F F
F
T
F
F
T
F
F F T T
T
T
F
F
F
T
F F T F
F
T
F
F
F
T
F F F T
T
T
F
F
F
F
F F F F
F
T
F
F
F
F

Step 4

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
T
F
T
T
T
T
T
T T T F
F
F
T
T
T
T
T
T T F T
T
F
T
T
T
T
F
T T F F
F
F
T
T
T
T
F
T F T T
T
T
T
F
F
T
T
T F T F
F
T
T
F
F
T
T
T F F T
T
T
T
F
F
F
F
T F F F
F
T
T
F
F
F
F
F T T T
T
T
F
F
T
T
T
F T T F
F
T
F
F
T
T
T
F T F T
T
T
F
F
T
F
F
F T F F
F
T
F
F
T
F
F
F F T T
T
T
F
F
F
T
T
F F T F
F
T
F
F
F
T
T
F F F T
T
T
F
F
F
F
F
F F F F
F
T
F
F
F
F
F

Step 5

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
T
T
F
T
T
T
T
T
T T T F
F
F
F
T
T
T
T
T
T T F T
T
T
F
T
T
T
T
F
T T F F
F
F
F
T
T
T
T
F
T F T T
T
T
T
T
F
F
T
T
T F T F
F
F
T
T
F
F
T
T
T F F T
T
F
T
T
F
F
F
F
T F F F
F
T
T
T
F
F
F
F
F T T T
T
T
T
F
F
T
T
T
F T T F
F
F
T
F
F
T
T
T
F T F T
T
F
T
F
F
T
F
F
F T F F
F
T
T
F
F
T
F
F
F F T T
T
T
T
F
F
F
T
T
F F T F
F
F
T
F
F
F
T
T
F F F T
T
F
T
F
F
F
F
F
F F F F
F
T
T
F
F
F
F
F

Step 6

P
Q
R
S
~
(
S
(
~
(
P
&
Q
)
R
)
)
T T T T
F
T
T
F
T
T
T
T
T
T T T F
T
F
F
F
T
T
T
T
T
T T F T
F
T
T
F
T
T
T
T
F
T T F F
T
F
F
F
T
T
T
T
F
T F T T
F
T
T
T
T
F
F
T
T
T F T F
T
F
F
T
T
F
F
T
T
T F F T
T
T
F
T
T
F
F
F
F
T F F F
F
F
T
T
T
F
F
F
F
F T T T
F
T
T
T
F
F
T
T
T
F T T F
T
F
F
T
F
F
T
T
T
F T F T
T
T
F
T
F
F
T
F
F
F T F F
F
F
T
T
F
F
T
F
F
F F T T
F
T
T
T
F
F
F
T
T
F F T F
T
F
F
T
F
F
F
T
T
F F F T
T
T
F
T
F
F
F
F
F
F F F F
F
F
T
T
F
F
F
F
F

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