“If I eat nuts， then I break out in hives.” This in turn can be symbolized a
s N——>H.
Next， we interpret the clause “there is a blemish on my hand” to mean “hives
，“ which we symbolize as H. Substituting these symbolssintosthe argument yie
lds the following diagram：
N——>H
H
Therefore， N
The diagram clearly shows that this argument has the same structure as the g
iven argument. The answer， therefore， is (B)。
Denying the Premise Fallacy
A——>B
~A
Therefore， ~B
The fallacy of denying the premise occurs when an if-then statement is prese
nted， its premise denied， and then its conclusion wrongly negated.
Example： (Denying the Premise Fallacy)
The senator will be reelected only if he opposes the new tax bill. But he wa
s defeated. So he must have supported the new tax bill.
The sentence “The senator will be reelected only if he opposes the new tax b
ill“ contains an embedded if-then statement： ”If the senator is reelected， t
hen he opposes the new tax bill.“ (Remember： ”A only if B“ is equivalent to
“If A， then B.”) This in turn can be symbolized as R——>~T. The sentence “But
the senator was defeated“ can be reworded as ”He was not reelected，“ which
in turn can be symbolized as ~R. Finally， the sentence “He must have support
ed the new tax bill“ can be symbolized as T. Using these symbols the argumen