2 1 conditional statements
This presentation is the property of its rightful owner.
Sponsored Links
1 / 19

2.1 Conditional Statements PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

2.1 Conditional Statements

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


2 1 conditional statements

2.1 Conditional Statements


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.

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

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

Negation ~

The negation of a statement is the

opposite of the original statement.

Symbol: ~pWords: not p

Examples: Find the negation of the statement.

  • This suit is black.

  • We are worthy.


Converse inverse and contrapostive

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

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

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 nie mack was a switch hitter

CONnie Mack was a SWITCH Hitter

Associate CONverse with SWITCHING the hypothesis and conclusion


Con verses help me do a flip

CONverses help me do a FLIP


The con vict switches his clothes once he escapes from jail

The CONvictSWITCHES his clothes once he escapes from jail.


N sync has a song no strings attached

N*Sync has a song NO strings attached

No Strings Attached


In verse think not

INverse think NOT


In digo is not blue or not purple

INdigo is not blue or not purple


If you are in dignant you are negative

If you are INdignant, you are NEGATIVE


Contrapositive

Contrapositive

  • You SWITCH and NEGATE the hypothesis and conclusion.

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


Fun fact

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

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

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 qSymbol: 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.


  • Login