Simplify the expression Simplify the expression 8(x+3)-4x-(x+1)8(x+3)-4x-(x+1)

a. 3x+2a. 3x+2 b. 3x+4b. 3x+4

c. 3x+23c. 3x+23 d. 3x+25d. 3x+25

2

1.8 warm-up 2

Simplify the expression Simplify the expression 8(x+3)-4x-(x+1)8(x+3)-4x-(x+1)

a. 3x+2a. 3x+2 b. 3x+4b. 3x+4

c. 3x+23c. 3x+23 d. 3x+25d. 3x+25

1.8 warm-up

2

2.1 Conditional Statements

You will determine the validity of a conditional statement and its converse. You will also find

counterexamples to disprove statements that are false.

PardekooperPardekooper

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Conditional StatementsConditional StatementsIf-then Statement:

one statement depends on the result of a condition.

Example:Example:

''If Deanna eats the last cookie, then Leon will buy more.'‘

hypothesishypothesis conclusionconclusion

hypothesis conclusion

1st part,If ____

2nd part,then ____

If , then

You forgotp q

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Converse StatementsConverse Statements

switch the hypothesis and the conclusion

Example:Example:

''If Leon buys some more cookies, then Deanna will eat the last one.'‘

conclusionconclusion hypothesishypothesis

conclusion hypothesis

1st part,If ____

2nd part,then ____

If , then

You forgotq pagain

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Lets try oneLets try one

ConditionalConditional

this had been an actual emergency

the attention signal you just heard would have been followed by official information, news, or instruction

hypothesis: conclusion:

If this had been an actual emergency, this had been an actual emergency, then the the attention signal you just heard would have been attention signal you just heard would have been followed by official information, news, or instruction.followed by official information, news, or instruction.

Note: The conditional of p →q where ‘→’ means ‘implies.’

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Lets try oneLets try one

ConverseConverse

this had been an actual emergency

the attention signal you just heard would have been followed by official information, news, or instruction

hypothesis: conclusion:

If the attention signal you just heard would have been the attention signal you just heard would have been followed by official information, news, or instructionfollowed by official information, news, or instruction , , then this had been an actual emergency.this had been an actual emergency.

Note: The converse of p →q is q → p. ‘→’ means ‘implies.’

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Negation StatementsNegation Statements

the denial of a statement

If a statement is true,

then its negation is

false.

If a statementis false,then its

negation istrue.

MeadowsMeadows

&&

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Negation StatementsNegation StatementsExample: .

this had not been an actual emergency

the attention signal you just heard would not have been followed by official information, news, or instruction

hypothesis: conclusion:

IfIf this hadthis had notnot been an actual emergencybeen an actual emergency, then, then the attention signal you just heard wouldthe attention signal you just heard would not not

have been followed by official information, news, have been followed by official information, news, or instruction.or instruction.

Note: The inverse of p → q is ~p → ~q. ‘~’ means ‘not.’

this had not been an actual emergency

the attention signal you just heard would not have been followed by official information, news, or instruction

conclusion:

hypothesis:

IfIf the attention signal you just heard wouldthe attention signal you just heard would notnot have been followed have been followed by official information, news, or instructionby official information, news, or instruction, then, then this hadthis had notnot been been an actual emergencyan actual emergency..

Note: The contrapositive of p → q is ~ q → ~ p.

Contrapositive Contrapositive StatementsStatements

created by negating the hypothesis and conclusion of the converse of the given

conditional.

Identify the hypothesis and conclusion of each conditional.

2. If you want to be fit, then you want to get plenty of excise.

4. “If you can see the magic in a fairy tale, you can face the future,”

6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach

8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”--Georgia O’Keeffe, artist

Write each statement as a conditional. {if-then}

10. 3x-7=14 implies that 3x=21.

12. All obtuse angles have measure greater than 90o.

14. Two skew lines do not lie in the same plane.

Show that each conditional is false by giving a counterexample.

16. Odd integers less than 10 are prime.

18. If you play sports with a ball and bat, then you play baseball.

2.1 Assignment 2.1 Assignment

page 83-86 even {2-32, 48-51, omit page 83-86 even {2-32, 48-51, omit 20,22}20,22}

2.1 Assignment 2.1 Assignment

page 83-86 even {2-32, 48-51, omit page 83-86 even {2-32, 48-51, omit 20,22}20,22}

Write the converse of each conditional. {switch the hyp with conclusion}

24. If a triangle is a right triangle, then it has a 900 angle.

26. If you do not work, then you do not get paid.

Write the converse, then determine if the conditional and converse are true or false.

28. If a point is in the first quadrant, then its coordinates are positive.

30. If the probability that an event will occur is 1, then the event is certain to occur.

32. If two angles has a measure 900, then the angles are congruent.

Write the words for the symbolic ststements shown. Determine the truth value of the statement. If false, provide a counterexample.

p: A figure is square. q: A figure has four congruent angles.

r; A figure has four congruent sides

48. p q 49.q p 50. r q 51. (q and r) p

2.1 Assignment 2.1 Assignment

page 83-86 even {Omit 20,22page 83-86 even {Omit 20,22

Identify the hypothesis and conclusion of each conditional.

2. If you want to be fit, then you want to get plenty of excise.

4. “If you can see the magic in a fairy tale, you can face the future,”

6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach

8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”--Georgia O’Keeffe, artist

Write each statement as a conditional. {if-then}

10. If 3x-7=14 , then 3x=21.

12. If you have an obtuse angles , then the measure is greater than 90o.

14. If you have two skew lines, then they do not lie in the same plane.

Show that each conditional is false by giving a counterexample.

16. 4, 6, 8, 9

18. softball

2.1 Conditional StatementsGeometry

Identify the hypothesis and conclusion of each conditional.

2. If you want to be fit, then you want to get plenty of excise.

4. “If you can see the magic in a fairy tale, you can face the future,”

6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach

8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”--Georgia O’Keeffe, artist

Write each statement as a conditional. {if-then}

10. If 3x-7=14 , then 3x=21.

12. If you have an obtuse angles , then the measure is greater than 90o.

14. If you have two skew lines, then they do not lie in the same plane.

Show that each conditional is false by giving a counterexample.

16. 4, 6, 8, 9

18. softball