To symbolize this argument, let the clause “he is innocent” be denoted by I,
and let the clause “when we hold him under water for sixty seconds he will
not drown“ be denoted by ~D. Then the argument can be symbolized as
I——>~D
~D
Therefore, I
Notice that this argument is fallacious: the conclusion “he is innocent” is
also a premise of the argument. Hence the argument is circular——it proves wh
at was already assumed. The argument affirms the conclusion then invalidly u
ses it to deduce the premise. The answer will likewise be fallacious.
We start with answer-choice (A)。 The sentence
“To insure that the remaining wetlands survive, they must be protected by th
e government“
contains an embedded if-then statement:
“If the remaining wetlands are to survive, then they must be protected by th
e government.“
This can be symbolized as S——>P. Next, the sentence “This particular wetland
is being neglected“ can be symbolized as ~P. Finally, the sentence ”It will
soon perish“ can be symbolized as ~S. Using these symbols to translate the
argument gives the following diagram:
S——>P
~P
Therefore, ~S
The diagram clearly shows that this argument does not have the same structur
e as the given argument. In fact, it is a valid argument by contraposition.
Turning to (B), we reword the statement “when I eat nuts, I break out in hiv
es“ as