What You'll Learn
To help you read critically, as in Example 7
You have heard if-then statements such as this one:
If you are not completely satisfied, then your money will be refunded.
Another name for an if-then statement is aEvery conditional has two parts. The part following if is the and the part following then is the
Identifying the Hypothesis and the Conclusion
Identify the hypothesis and the conclusion of this conditional statement:
If today is the first day of fall, then the month is September.
Hypothesis: Today is the first day of fall.
Conclusion: The month is September.
You can write many sentences as conditionals.
Writing a Conditional
Write each sentence as a conditional.
A rectangle has four right angles.
If a figure is a rectangle, then it has four right angles.
A tiger is an animal.
If something is a tiger, then it is an animal.
A conditional can have aof true or false. To show that a conditional is true, show that every time the hypothesis is true, the conclusion is also true. To show that a conditional is false, you need to find only one counterexample for which the hypothesis is true and the conclusion is false.
Finding a Counterexample
Show that this conditional is false by finding a counterexample:
If it is February, then there are only 28 days in the month.
To show that this conditional is false, you need to find one counterexample that makes the hypothesis true and the conclusion false.
February in the year 2008 is a counterexample. Because 2008 is a leap year, the month of February has 29 days.
The conditional is false because February 2008 is a counterexample.
You can use a Venn diagram to better understand true conditional statements.
Using a Venn Diagram
Draw a Venn diagram to illustrate this conditional:
If you live in Chicago, then you live in Illinois.
The set of things that satisfy the hypothesis lies inside the set of things that satisfy the conclusion.