Post on 03-Jan-2016
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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
PardekooperPardekooper
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.’
PardekooperPardekooper
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