Chapter_2.3_Conditional_Statements

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Chapter 2.3
Conditional Statements
Objective: Be able to recognize conditional statements and
write converse, inverse and countrapositive statements
Check.4.16
Use inductive reasoning to write conjectures and/or conditional statements
Develop an understanding of the tools of logic and proof, including aspects of
CLE 3108.4.3
formal logic as well as construction of proofs.
Identify, write, and interpret conditional and bi-conditional statements along with
Check.4.15
the converse, inverse, and contra-positive of a conditional statement.
Conditional Statements -
process
If – then
 Hypothesis – Conclusion





If you finish high school then
you increase your lifetime earning potential by
$1million
If you finish college then
you increase your lifetime earning potential by
$3million
Conditional Statements
If – then
 Hypothesis – Conclusion


If points A, B, and C lie on a line then they are collinear.

An angle with a measure greater than 90 is an obtuse angle.
Perpendicular lines intersect
Two lines are
perpendicular
They intersect
Conditional Statements – Truth?

Statement – if you get 100%, then your
teacher will give you an A
TRUE
If you get 100% correct, your teacher gives you
an A.
False
 If you get 100% correct, your teacher gives you
a B.
True, can’t say not
 You get 98%, your teacher gives you an A.
 You get 85% correct then your teacher gives you
a B.
True, can’t say not

Conditional Statements
Statement
Statement
Conditional
Conditional
Formed
Formed by
by
Given
hypothesis
Given hypothesis
and
and conclusion
conclusion
Converse
Converse
Exchanging
Exchanging
hypothesis
hypothesis and
and
conclusion
conclusion
Inverse
Inverse
Negate
Negate both
both
hypothesis
hypothesis and
and
conclusion
conclusion
Contrapositive
Contrapositive
Negate
Negate both
both
hypothesis
hypothesis and
and
conclusion
of
conclusion of
converse
converse
Symbols
Symbols
pq
pq
qp
qp
~p~q
~p~q
~q~p
~q~p
Example
Example
If
two angles
angles have
have the
If two
the
same
same measure
measure they
they are
are
congruent
congruent
If
If two
two angles
angles are
are
congruent,
congruent, then
then they
they have
have
the
same
measure
the same measure
If
If two
two angles
angles do
do not
not have
have
the
the same
same measure,
measure, then
then
they
are
not
congruent
they are not congruent
If two angles are not
congruent, then they do not
have the same measure
Conditional Statements

Conditional Statement
If two angles form a linear pair, then they are supplementary.

Converse Statement



Inverse Statement



If two angles are supplementary, they form a linear pair
FALSE
If two angles do not form a linear pair, then they are not
supplementary
False
Contrapositive


If two angles are not supplementary, they do not form a linear
pair.
True
Practice Assignment

Page 111, 40 - 62 Even
Check your practice
Page 111, 40 - 62 Even
40. True
42. False
44. False
46. True
48. Converse: If a bird cannot fly, then it



is an ostrich. false. Counterexample:
The bird could be a penguin.
Inverse: If a bird is not an ostrich,
then it can fly. The inverse is false.
Counterexample: The bird could be a
penguin.
Contrapositive: If a bird can fly, then
the bird is not an ostrich; true.
50. If a figure is a rectangle, then
it is a square. false.

If a figure is not a square,

false.
If a figure is not a rectangle,
then it is not a square. true.
then it is not a rectangle.
54. Converse true
56. Contrapositive False
60. False
62.
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