2-2 Conditional Statements

Learning Target: IWBAT understand conditional statements and their parts

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Success Criteria:

• Recognize conditional statements and the parts of a conditional statement
• Formulate conditional statements
• To analyze the truth value of a conditional statement

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Entry Task

• The sequence 1,1,2,3,5,8,13,21,… is known as the Fibonacci Sequence. Make a conjecture about the sequence and predict the next two terms.
• Find a counterexample for the following statement:

Conditional statements

• A conditional statement is an “if-then” statement
• Examples:
• If you study, then you will get good grades.

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Parts of a conditional statement

• Hypothesis: the part following “if”
• written as p
• Conclusion: the part following “then”
• written as q

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p→ q means “if p, then q” or “p implies q”

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Examples

Identify the hypothesis and conclusion

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• If an animal is a robin, then it is a bird.
• The Tigers will play in the tournament if they win the next game.
• If an angle measures 130 degrees, then it is obtuse.

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Diagram of p→ q

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The inner circle represents the hypothesis (p) and the outer circle represents the conclusion (q).

Example

What conditional statement does the diagram represent?

Writing a conditional

You can re-write a statement as a conditional statement by first identifying the hypothesis and conclusion.

Example: Vertical angles share a vertex

Example

Find the truth value of each statement. If false, what is a counterexample?

• If two angles form a linear pair, then they are supplementary.

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Finding the truth value of a conditional

• Truth value is whether the statement is true or false.
• It is false if you can find a counterexample

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Ex: If a number is divisible by 3, then it is odd.

Is this true or false? Why?

Group Activity

• Write a conditional statement
• Identify the hypothesis and conclusion
• Draw a diagram
• What is the truth value of your statement? If false, give a counterexample.