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Lesson 2-3Lesson 2-3Conditional Conditional StatementsStatements
Ohio Content Standards:
Ohio Content Standards:
Apply mathematical knowledge and skills routinely in other content areas and practical
situations.
Ohio Content Standards:Apply reasoning processes and
skills to construct logical verifications or counter-examples to test conjectures and to justify
and defend algorithms and solutions.
Ohio Content Standards:Use a variety of mathematical representations flexibly and
appropriately to organize, record and communicate mathematical
ideas.
Ohio Content Standards:Write clearly and coherently
about mathematical thinking and ideas.
Conditional Statement
Conditional Statement
A statement that can be written in if-then form.
If-Then Statement
If-Then Statement
Written in the form if p, then q.
Hypothesis
Hypothesis
The phrase immediately following the word if.
Conclusion
Conclusion
The phrase immediately following the word then.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement.conclusion of each statement.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement.conclusion of each statement.
• If a polygon has 6 sides, then it is a If a polygon has 6 sides, then it is a hexagon.hexagon.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement.conclusion of each statement.
• If a polygon has 6 sides, then it is a If a polygon has 6 sides, then it is a hexagon.hexagon.
• Tamika will advance to the next level Tamika will advance to the next level of play if she completes the maze in of play if she completes the maze in her computer game.her computer game.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement. conclusion of each statement.
Then write the statement in the if-Then write the statement in the if-then form.then form.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement. conclusion of each statement.
Then write the statement in the if-Then write the statement in the if-then form.then form.
• Distance is positive.Distance is positive.
Identify the hypothesis and Identify the hypothesis and conclusion of each statement. conclusion of each statement.
Then write the statement in the if-Then write the statement in the if-then form.then form.
• Distance is positive.Distance is positive.
• A five-sided polygon is a pentagon.A five-sided polygon is a pentagon.
Determine the truth value of the Determine the truth value of the following statement for each set of following statement for each set of
conditions.conditions. If Yukon rests for 10 days, his ankle If Yukon rests for 10 days, his ankle
will heal.will heal.
Determine the truth value of the Determine the truth value of the following statement for each set of following statement for each set of
conditions.conditions. If Yukon rests for 10 days, his ankle If Yukon rests for 10 days, his ankle
will heal.will heal.
• Yukon rests for 10 days, and he still Yukon rests for 10 days, and he still has a hurt ankle.has a hurt ankle.
Determine the truth value of the Determine the truth value of the following statement for each set of following statement for each set of
conditions.conditions. If Yukon rests for 10 days, his ankle If Yukon rests for 10 days, his ankle
will heal.will heal.
• Yukon rests for 3 days, and he still Yukon rests for 3 days, and he still has a hurt ankle.has a hurt ankle.
Determine the truth value of the Determine the truth value of the following statement for each set of following statement for each set of
conditions.conditions. If Yukon rests for 10 days, his ankle If Yukon rests for 10 days, his ankle
will heal.will heal.
• Yukon rests for 10 days, and he Yukon rests for 10 days, and he does not have a hurt ankle anymore.does not have a hurt ankle anymore.
Determine the truth value of the Determine the truth value of the following statement for each set of following statement for each set of
conditions.conditions. If Yukon rests for 10 days, his ankle If Yukon rests for 10 days, his ankle
will heal.will heal.
• Yukon rests for 7 days, and he does Yukon rests for 7 days, and he does not have a hurt ankle anymore.not have a hurt ankle anymore.
Related Conditionals
Related Conditionals
Statements based on a given conditional
statement.
Conditional
Conditional
Given the hypothesis and conclusion.
Converse
Converse
Exchanging the hypothesis and conclusion of the
conditional.
Inverse
Inverse
Negating both the hypothesis and conclusion
of the conditional.
Contrapositive
Contrapositive
Negating both the hypothesis and conclusion
of the converse statement.
Logically Equivalent
Logically Equivalent
Statements with the same truth values.
Write the converse, inverse, and Write the converse, inverse, and contrapositive of the statement:contrapositive of the statement:
All squares are rectangles.All squares are rectangles.
Determine whether each statement is Determine whether each statement is truetrue or or falsefalse. If a statement is false, . If a statement is false,
give a counterexample.give a counterexample.
Assignment:Assignment:
Pgs. 78 - 80 Pgs. 78 - 80 16-44 evens, 16-44 evens, 52-64 evens52-64 evens
