Mirrored from philosophy.hku.hk/think/
Critical Thinking Web

Answer to exercise #1d

Step 1

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
T
T
T
T
T T F
T
T
T
F
T F T
T
T
F
T
T F F
T
T
F
F
F T T
F
F
T
T
F T F
F
F
T
F
F F T
F
F
F
T
F F F
F
F
F
F

Step 2

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
T
F
T
T
F
T
T T F
T
F
T
T
T
F
T F T
T
F
T
F
F
T
T F F
T
F
T
F
T
F
F T T
F
T
F
T
F
T
F T F
F
T
F
T
T
F
F F T
F
T
F
F
F
T
F F F
F
T
F
F
T
F

Step 3

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
T
F
T
T
T
F
T
T T F
T
F
T
T
T
T
F
T F T
T
F
T
F
F
F
T
T F F
T
F
T
F
F
T
F
F T T
F
T
F
T
T
F
T
F T F
F
T
F
T
T
T
F
F F T
F
T
F
T
F
F
T
F F F
F
T
F
T
F
T
F

Step 4

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
T
T
F
T
T
T
F
T
T T F
T
T
F
T
T
T
T
F
T F T
T
F
F
T
F
F
F
T
T F F
T
F
F
T
F
F
T
F
F T T
F
F
T
F
T
T
F
T
F T F
F
F
T
F
T
T
T
F
F F T
F
F
T
F
T
F
F
T
F F F
F
F
T
F
T
F
T
F

Step 5

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
F
T
T
F
T
T
T
F
T
T T F
F
T
T
F
T
T
T
T
F
T F T
T
T
F
F
T
F
F
F
T
T F F
T
T
F
F
T
F
F
T
F
F T T
T
F
F
T
F
T
T
F
T
F T F
T
F
F
T
F
T
T
T
F
F F T
T
F
F
T
F
T
F
F
T
F F F
T
F
F
T
F
T
F
T
F

Step 6

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
F
T
T
F
T
T
T
T
F
T
T T F
F
T
T
F
T
T
T
T
T
F
T F T
T
T
F
F
T
F
F
F
F
T
T F F
T
T
F
F
T
F
F
T
T
F
F T T
T
F
F
T
F
T
T
F
F
T
F T F
T
F
F
T
F
T
T
T
T
F
F F T
T
F
F
T
F
T
F
F
F
T
F F F
T
F
F
T
F
T
F
T
T
F

Step 7

P
Q
R
~
(
~
(
P
↔
(
~
P
∨
Q
)
)
 →
~
R
)
T T T
F
F
T
T
F
T
T
T
T
F
T
T T F
F
F
T
T
F
T
T
T
T
T
F
T F T
T
T
T
F
F
T
F
F
F
F
T
T F F
F
T
T
F
F
T
F
F
T
T
F
F T T
T
T
F
F
T
F
T
T
F
F
T
F T F
F
T
F
F
T
F
T
T
T
T
F
F F T
T
T
F
F
T
F
T
F
F
F
T
F F F
F
T
F
F
T
F
T
F
T
T
F