2-1 CONDITIONAL STATEMENTS

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2-1 CONDITIONAL STATEMENTS A statement in the form “If _____, then _______.” is called a Conditional Statement A conditional statement has two parts: If ______________ , then _______________ . hypothesis conclusion

Ex1: If today is Monday, then yesterday was Sunday. Examples: Identify the Hypothesis and Conclusion of each conditional statement. Ex1: If today is Monday, then yesterday was Sunday. Hypothesis: Today is Monday. Conclusion: Yesterday was Sunday.

Ex2. If x = 5, then 2x = 10. Hypothesis: x = 5 Conclusion: 2x = 10. Examples: Identify the Hypothesis and Conclusion of each conditional statement. Ex2. If x = 5, then 2x = 10. Hypothesis: x = 5 Conclusion: 2x = 10. Ex3. If x = 6, then x2 = 36. Hypothesis: x = 6 Conclusion: x2 = 36.

Rewriting conditional statements into the “if…then…” format. Ex4) 3x + 2 = -13 implies that x = -5. Rewrite as “If 3x + 2 = -13, then x = -5.” Hypothesis: 3x + 2 = -13 Conclusion: x = -5

Ex5) A number is divisible by 2 if it is divisible by 6. Rewrite as “If a number is divisible by 6, then it is divisible by 2.” Hypothesis: A number is divisible by 6. Conclusion: The number is divisible by 2.

CONVERSE STATEMENTS To find the converse of a conditional statement, you switch the hypothesis and conclusion. Ex6: If today is Monday, then yesterday was Sunday. Hypothesis: Today is Monday. Conclusion: Yesterday was Sunday. Converse: If yesterday was Sunday, then today is Monday.

Not all converses will be true!! Ex7. If you live in Doylestown, then you live in Pennsylvania. Hypothesis: You live in Doylestown. Conclusion: You live in Pennsylvania. Converse: If you live in Pennsylvania, then you live in Doylestown. Is this converse true? No.

In order to prove the converse is false, you must provide a counterexample. A counterexample is an example for which the hypothesis is true, but the conclusion is false. Counterexample: You live in Chalfont.

Ex8) a) Hypothesis: x = -5 Conclusion: b) Converse: False Example: For the conditional statement, identify the hypothesis and conclusion, write the converse of the statement and determine if the converse is true or false. c) If the converse is false, provide a counterexample. Ex8) a) Hypothesis: x = -5 Conclusion: b) Converse: False c) Counterexample: x = 5.

Biconditional Statements use the phrase “if and only if” to indicate when a conditional and its converse are both true. If tomorrow is Thursday, then today is Wednesday. Rewrite: Tomorrow is Thursday if and only if, today is Wednesday.

Ex1. Congruent segments are segments that have equal lengths. You can rewrite definitions as biconditionals. Ex1. Congruent segments are segments that have equal lengths. Segments are congruent if and only if their lengths are equal. Ex2. Coplanar points are points all in one plane. Points are coplanar if and only if they all lie in one plane.

Section 3-6 Inductive Reasoning vs. Deductive Reasoning

Deductive Reasoning General to Specific Definition: Drawing conclusions based on accepted statements (theorems, given information, etc). Deductive Reasoning takes General Rules and applies them to Specific Events. General to Specific

Inductive Reasoning Specific to General Definition: Drawing conclusions based on several past experiences and observations. Inductive Reasoning takes Specific Events and Observations and applies them to conclude General Rules. KEY WORD: OBSERVE Specific to General