The original statement, “If p, then q,” is a general form that covers such
statements as the following:
Of the three Roman numeral options in Example 4, only one necessarily
follows. Take a look at the options one at a time:
Can you see that none of these statements—not even number 3—necessarily
follows from the original?
(C) I and II only
(D) I and III only
(E) I, II, and III
If you live in Alabama, then you live in the United States (p = “live in
Alabama”; q = “live in U.S.”).
1.
2. All prime numbers are integers (p = “is prime”; q = “is an integer”).
If Marla studies, she will get an A on the test (p = “studies”; q = “gets an
A”).
3.
If q, then p. This is not necessarily so. You cannot simply switch the p and
the q. Look what illogical results you would get with the three samples
above:
I.
1. If you live in the United States, then you live in Alabama.
2. All integers are prime numbers.
3. If Marla gets an A on the test, then she must have studied.
If not p, then not q. This is not necessarily so. You cannot simply negate
both the p and the q. Look what illogical results you would get with the
three samples above: