Name:
Date:
Period:
Secondary Math I – 16.2: Understanding Conditional Statements, Arguments, and Truth Tables
Mr. Heiner
1. Read the pair of statements. Then write a value conclusion.
Statement: If you hear thunder, there must be lightning.
Statement: You hear thunder.
Conclusion:
2. Read the conditional statement and conclusion. Then write the addition statement required to reach the
conclusion.
Conditional Statement: If Jonas and Gabriel are the same age, it is April.
Statement:
Conclusion: Therefore, Jonas and Gabriel are not the same age.
3. Consider the conditional statement “If I complete my homework, then I receive extra credit in class.”
a. What is the hypothesis, p? What is the conclusion, q?
Hypothesis, p:
Conclusion, q:
b. Assume that p is true and q is true. What is the truth value of this statement? Explain what this means in terms of
the problem situation.
c. Assume that p is true and q is false. What is the truth value of this statement? Explain what this means in terms of
the problem situation.
d. Assume that p is false and q is true. What is the truth value of this statement? Explain what this means in terms of
the problem situation.
e. Assume that p is false and q is false. What is the truth value of this statement? Explain what this means in terms of
the problem situation.
f. Complete the truth table.
𝑝
𝑞
𝑝↦𝑞
4. Consider the conditional statement “If an organism can perform photosynthesis, then the organism is a plant.”
a. Identify the hypothesis, p:
b. Identify the conclusion, q:
c. Is the conditional statement true? Explain your reasoning.
d. Identify the converse.
e. Is the converse true? Explain your reasoning.
5. Consider the conditional statement “If Agioso is in his room, then he is in his house.”
a. Is the conditional statement true?
b. Identify the negation of the hypothesis.
c. Identify the negation of the conclusion.
d. Write the inverse of the conditional statement.
e. Is the inverse true? Explain your reasoning.
6. Consider the conditional statement “If Molly is a teenager, she is 13 years old.”
a. Is the conditional statement true? Explain your reasoning.
b. Write the contrapositive of the conditional statement.
c. Is the contrapositive true? Explain your reasoning.
d. Can this conditional statement be rewritten as a true biconditional statement? If yes, rewrite it as a bicondtional
statement. If no, explain why not.
7. Complete each sentence.
a. If a conditional statement is true, then its converse…
b. If a conditional statement is false, then its converse…
c. If a conditional statement is true, then its inverse…
d. If a conditional statement is false, then its inverse…
e. If a conditional statement is true, then its contrapositive…
f.
If a conditional statement is false, then its contrapositive…
g. A conditional statement and its
are logically equivalent.