SAT Subject Test Mathematics Level 1

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:

II.