Questioning Strategies
Analytic Geometry Student Notes 1.4
AKS: Identify, write, and analyze conditional statements.
What should you be able to do?
 Identify, write, and analyze the truth value of conditional statements.
 Write the inverse, converse, and contrapositive of a conditional
statement.

When the word then does not
appear in a conditional
statement, how can you tell
which part is the conclusion?
Example: Identify the hypothesis and conclusion of each conditional.
a) If today is Thanksgiving Day, then today is Thursday.
Hypothesis (p): _________________________________________
Conclusion (q): _________________________________________
b) A number is a rational number if it is an integer.
Hypothesis (p): _________________________________________
Conclusion (q): _________________________________________
A conditional statement has a truth value of either true (T) or false (F). It is
false only when the hypothesis is true and the conclusion is false.

What are the steps you
should take to determine the
truth value of a conditional
statement?
To show that a conditional statement is false, you need to find only one
counterexample where the hypothesis is true and the conclusion is false.
Example: Determine if the conditional is true. If false, give a counterexample.
a) If this month is August, then next month is September.
Hypothesis: _______________
Conclusion: ________________
_______________________________________________________
b) If two angles are acute, then they are congruent.
Hypothesis: _______________
Conclusion: ________________
_______________________________________________________
c) If the sky is green, then 5 + 4 = 8.
Hypothesis: _______________
Conclusion: ________________
_______________________________________________________
Make a table that shows all the combinations of truth values for the hypothesis and conclusion and the resulting truth
values of the conditional statement. Explain a way to help you remember this.
Questioning Strategies
Analytic Geometry Student Notes 1.4
The negation of statement p is “not p,” written as ~p. The negation of a true
statement is false, and the negation of a false statement is true.

What are the chances that
either event p or event ~p
will occur? Explain.
Example: Write the negation of the following statements.
a) The answer is seven.
_______________________________________________________
b) The water was hot.
_______________________________________________________
Example: Write the converse, inverse, & contrapositive of the conditional
statement, than find the statement’s truth value:
If you go to Central Gwinnett, then you are a Black Knight.
p: ________________________________________________________
q: ________________________________________________________
Converse: __________________________________________________
______________________________________ Truth Value: ________
Inverse: ___________________________________________________
______________________________________ Truth Value: ________
Contrapositive: ______________________________________________
______________________________________ Truth Value: ________

Draw Example 1b as a
Venn Diagram.
Many sentences without the words if and then can be written as
conditionals. To do so, identify the sentence’s hypothesis and conclusion
by figuring out which part of the statement depends on the other.
Example: Write a conditional statement from the following.
a) An obtuse triangle has exactly one obtuse angle.
______________________________________________________
______________________________________________________
b) ____________________________
____________________________
____________________________
How can you remember the characteristics of the converse, inverse, and contrapositive of a conditional statement?