“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

t can be diagrammed as follows

R——>~T

~R

Therefore， T

[Note： Two negatives make a positive， so the conclusion ~（~T） was reduced to

T.] This diagram clearly shows that the argument is committing the fallacy

of denying the premise. An if-then statement is made； its premise is negated

； then its conclusion is negated.

Transitive Property

A——>B

B——>C

Therefore， A——>C

These arguments are rarely difficult， provided you step back and take a bir

d's-eye view. It may be helpful to view this structure as an inequality in m

athematics. For example， 5 > 4 and 4 > 3， so 5 > 3.

Notice that the conclusion in the transitive property is also an if-then sta

tement. So we don't know that C is true unless we know that A is true. Howev

er， if we add the premise “A is true” to the diagram， then we can conclude t

hat C is true：

A——>B

B——>C

A

Therefore， C

As you may have anticipated， the contrapositive can be generalized to the tr

ansitive property：

A——>B

B——>C

~C

Therefore， ~A

Example： （Transitive Property）

If you work hard， you will be successful in America. If you are successful i

n America， you can lead a life of leisure. So if you work hard in America， y

ou can live a life of leisure