epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

Basic Techniques To Prove
If/Then Statements
Let's start by looking at the details of a process that goes on
almost automatically in our minds hundreds of times every day—deciding
whether something is true or false. Suppose you make the following
statement:
If I go home this weekend^ I will take my parents out to dinner.
When is your statement true? When is it false; that is, when could you be
accused of lying?
The statement we are considering is a composite statement, and its two
parts are the following simple statements:
A: I go home this weekend.
B: I will take my parents out to dinner.
As far as your trip is concerned, there are two possibihties:
i. You are going home this weekend (A is true),
ii. You are not going home this weekend (A is false).
Regarding the dinner, there are two possibihties as well:
i. You will take your parents out to dinner (B is true),
ii. You will not take your parents out to dinner (B is false).