EXAMPLE 2.2.11

Select the statement that is a valid conclusion from the following premises, if a valid conclusion is warranted.

If I invest wisely, then I won't lose my money.

If I don't invest wisely, then I buy junk bonds.

If I read Investor's Weekly, then I won't buy junk bonds.

A. If I invest wisely, then I read Investor's Weekly.

B. If I buy junk bonds, then I don't invest wisely.

C. If I lose my money, then I don't read Investor's Weekly.

D. If I eat junk food, then I invest weakly.

E. None of these is warranted.

SOLUTION

Let p be the statement "I invest wisely."

Let q be the statement "I don't lose my money."

Let r be the statement "I buy junk bonds."

Let s be the statement "I read Investor's Weekly."

The premise scheme has this symbolic form:

1. p arrow q.

2. not p arrow r.

3. s arrow not r.

In order to use Transitive Reasoning, we want the first premise to be one whose antecedent is a variable that appears only one time. Since q appears only one time, we can replace the first premise with its equivalent contrapositive; we will then leave the second premise as it is, and replace the third premise with its contrapositive:

1. not q arrow not p.

2. not p arrow r.

3. r arrow not s.

Now we can form a valid argument:

not q arrow not p.

not p arrow r.

r arrow not s.

Therefore, not q arrow not s.

In words, the valid conclusion is "If I lose my money, then I didn't read Investor's Weekly." This is choice C. Another correct conclusion would be "If I read Investor's Weekly, then I don't lose my money."