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2-2 Conditional Statements

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Presentation on theme: "2-2 Conditional Statements"— Presentation transcript:

1 2-2 Conditional Statements

2 Examples If it is lightning, then practice will be cancelled
If it is 3:20, then school is over. If you have a daughter, then you are a parent If 2 lines intersect, then they do so at one point If 2 planes intersect, then they do so at a line.

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4 If p, then q. Hypothesis Conclusion
These statements are called IF-THEN statements, or more formally known as CONDITIONALS. If p, then q. Hypothesis Conclusion

5 The words after IF and before THEN are part of the hypothesis.
The words after THEN are part of the conclusion YOU DO NOT INCLUDE IF or THEN in either the hypothesis or the conclusion.

6 The TRUTH VALUE of a conditional is either true or false.
In order to show a conditional is true, show that every time the hypothesis is true, the conclusion is also true. To show that conditional is false, you must find at least one counterexample for which the hypothesis is true and the conclusion is false.

7 The NEGATION of a statement p is the opposite of the statement
The NEGATION of a statement p is the opposite of the statement. The symbol is ~p and is read “not p”. If you say the water is cold, the negation would be “the water is not cold” You use negations to write statements that are related to conditionals. Each conditional has 3 other statements that are closely related to the original conditional statement.

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9 If you live in Ohio, then you live in Lima.
Is this always true? What is one counterexample? Can you write the converse, inverse, and contrapositive? Identify the truth values of each.

10 Converses and counterexamples
If you live in Lima, OH, then you live north of the Ohio River. Can you write the converse, inverse, and contrapositive? Identify the truth values of each.

11 If an angle is acute, then its measurement is less than 180.
ORIGINAL Conditional If an angle is acute, then its measurement is less than 180. Converse Inverse Contrapositive

12 If two angles are adjacent, then they share a vertex.
ORIGINAL Conditional If two angles are adjacent, then they share a vertex. Converse Inverse Contrapositive

13 When you find two statements that have the same truth value, then the statements are equivalent statements. Many texts refer to these statements being LOGICALLY EQUIVALENT (LE). Conditionals and contrapostives are always LE. Converses and Inverses are always LE.

14 HWK Section 2.2 in MathXLforSchool

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