CONTRAPOSITIVE
“If p, then q,” is logically equivalent to “If not q, then not p.”Can you see that none of these statements necessarily follows from the
original statement?
These three statements are all as true as the originals they’re based on. So of
the three options, only III is true, and the answer is (B).
TRANSLATING FROM ENGLISH INTO ALGEBRA
Solving a word problem means taking a situation that is described verbally
and turning it into one that is described mathematically. It means translating
from English into algebra, which is exactly what Example 5 asks you to do.
1. If you don’t live in Alabama, then you don’t live in the United States.
2. If a number’s not prime, then it’s not an integer.
3. If Marla doesn’t study, then she won’t get an A.If not q, then not p. This is true. If you both switch the p and q and negate
them, the result is logically equivalent to the original. This is the
contrapositive. Here are the contrapositives of the three samples above:III.
1. If you don’t live in the United States, then you don’t live in Alabama.
2. If a number’s not an integer, then it’s not a prime number.
3. If Marla doesn’t get an A on the test, then she must not have studied.