1.8 warm-up 2
Simplify the expression
8(x+3)-4x-(x+1)
a. 3x+2
b. 3x+4
c. 3x+23
d. 3x+25
2
1.8 warm-up
Simplify the expression
8(x+3)-4x-(x+1)
a. 3x+2
b. 3x+4
c. 3x+23
d. 3x+25
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.
Pardekooper
Conditional Statements
If-then Statement:
You forgot
p
q
one statement depends on the result of a condition.
If hypothesis , then conclusion
Example:
1st part,
2nd part,
If''If____
thenmore.'‘
____
Deanna eats the last cookie, then Leon will buy
hypothesis
Pardekooper
conclusion
Converse Statements
You forgot
q
p
switch the hypothesis and the conclusion
again
If conclusion , then hypothesis
Example:
1st part,
2nd part,
If Leon
____buys some more cookies, then Deanna will eat the
then
''If
last____
one.'‘
conclusion
Pardekooper
hypothesis
Lets try one
hypothesis:
this had been an actual
emergency
conclusion:
the attention signal you just heard
would have been followed by
official information, news, or
instruction
Conditional
If this had been an actual emergency, then the
attention signal you just heard would have been
followed by official information, news, or instruction.
Note: The conditional of p →q where ‘→’ means ‘implies.’
Pardekooper
Lets try one
hypothesis:
this had been an actual
emergency
conclusion:
the attention signal you just heard
would have been followed by
official information, news, or
instruction
Converse
If the attention signal you just heard would have been
followed by official information, news, or instruction,
then this had been an actual emergency.
Note: The converse of p →q is q → p. ‘→’ means ‘implies.’
Pardekooper
Negation Statements
the denial of a statement
If a statement
is true,
then its
negation is
false.
Pardekooper
If a statement
is false,
then its
negation is
true.
Negation Statements
Example: .
hypothesis:
this had not been an actual
emergency
conclusion:
the attention signal you just heard
would not have been followed by
official information, news, or
instruction
If this had not been an actual emergency, then
the attention signal you just heard would not
have been followed by official information, news,
or instruction.
Meadows
&
Pardekooper
Note: The inverse of p → q is ~p → ~q. ‘~’ means ‘not.’
Contrapositive Statements
created by negating the hypothesis and
conclusion of the converse of the given
conditional.
conclusion:
hypothesis:
this had not been an actual emergency
the attention signal you just heard would
not have been followed by official
information, news, or instruction
If the attention signal you just heard would not have been followed
by official information, news, or instruction, then this had not been
an actual emergency.
Note: The contrapositive of p → q is ~ q → ~ p.
2.1 Assignment
page 83-86 even
{2-32, 48-51, 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. 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
page 83-86 even
{2-32, 48-51, omit 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
page 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
Geometry
2.1 Conditional Statements
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