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# 2.1 Conditional Statements - PowerPoint PPT Presentation

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

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.

• 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 ~ parts.

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 parts. 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 parts.

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

CON are a musician. nie Mack was a SWITCH Hitter

Associate CONverse with SWITCHING the hypothesis and conclusion

CON are a musician. verses help me do a FLIP

The are a musician. CONvictSWITCHES his clothes once he escapes from jail.

N are a musician. *Sync has a song NO strings attached

No Strings Attached

IN are a musician. verse think NOT

IN are a musician. digo is not blue or not purple

If you are are a musician. INdignant, you are NEGATIVE

Contrapositive are a musician.

• You SWITCH and NEGATE the hypothesis and conclusion.

• It is like taking the converse and inverse at the same time.

Fun Fact are a musician.

• 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 are a musician.

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 are a musician. 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.