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2.1 Conditional Statements. Conditional Statement – a logical statement with two parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If p, then q is symbolized as p -> q (p implies q). Ex: If you study hard, then you will get As.

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## 2.1 Conditional Statements

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**Conditional Statement – a logical statement with two**parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If p, then q is symbolized as p -> q (p implies q). Ex: If you study hard, then you will get As. If you live in Ridgewood, then you live in NJ. If an angle is 28 degrees, then it is acute.**Rewrite into “If, then” form**• All fruits have seeds. • Two angles that add up to 180 degrees are supplementary. • An even number is a number divisible by 2. • 3x + 17 = 23, because x = 2. • Only people who are 18 are allowed to vote. • P=It is raining. Q =I must bring an umbrella. • Today is Friday and tomorrow is Saturday. Now go back and underline the hypothesis and circle the conclusions.**Negation ~**The negation of a statement is the opposite of the original statement. Symbol: ~p Words: not p Examples: Find the negation of the statement. • This suit is black. • We are worthy.**Converse, Inverse and Contrapostive**Given Conditional Statement: p->q Converse: Switch hypothesis and conclusion. q->p Inverse: Negate hypothesis and conclusion. ~p->~q Contrapositive: Switch and negate the hypothesis and conclusion. ~q->~p**Counterexamples**A counterexample is a case that fits the hypothesis but leads to a different conclusion. You can prove a statement is false by finding a counterexample. Practice finding counterexamples. 1) If a number is prime, then it is odd. 2) If you live in Ridgewood, you go to RHS. 3) If a food is round, then it is pizza. 4) If a 3D figure lacks vertices, it is a sphere.**Conditional Statement: If you are a guitar player, then you**are a musician. Converse: If you are a musician, then you are a guitar player. T or F Inverse: If you are not a guitar player, then you are not a musician. T or F Contrapositive. If you are not a musician, then you are not a guitar player. T or F**CONnie Mack was a SWITCH Hitter**Associate CONverse with SWITCHING the hypothesis and conclusion**N*Sync has a song NO strings attached**No Strings Attached**Contrapositive**• You SWITCH and NEGATE the hypothesis and conclusion. • It is like taking the converse and inverse at the same time.**Fun Fact**• A conditional statement and its contrapositive are either both true or false. They are equivalent statements. • A converse statement and an inverse statement are also both true or false. They are also equivalent statements. • But (for example), a conditional may be true and a converse may be false.**Guided Practice**Everyone will have to share, so make sure you come up with something. • Write the definition of perpendicular lines as a conditional statement. Is the converse true? • Come up with your own conditional statement. Then find the converse, inverse and contrapositive. • Write true or false next to each of the four statements you wrote in number 2.**Biconditional Statements**When a conditional statement and its converse are true, you can write them as a single biconditional statement linking the hypothesis and conclusion with “if and only if”. Words: p if and only if q Symbol: p <-> q Write a biconditional statement for your conditional statement if both your conditional and converse were true. If not, write one for perpendicular lines.

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