23 Conditional Statements Real Life If you would like to speak to a representative press 0 now Vocabulary Conditional Statement a statement that can be written in ifthen form Ifthen statement ID: 421741
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Slide1
Ms. Andrejko
2-3 Conditional StatementsSlide2
Real Life
If you would like to speak to a representative press 0 nowSlide3
Vocabulary
Conditional Statement-
a statement that can be written in
if-then
form If-then statement- is of the form if p, then
q
Hypothesis-
the phrase immediately following the word
if
Conclusion-
the phrase immediately following the word
then
Related Conditionals-
other statements that are based on a given conditional statement
Logically equivalent-
Statements with the same truth valuesSlide4
Notation
p
q
= if
p
, then
q
p
= hypothesis
q
= conclusionSlide5
Conditional Truth Table
p
q
p
q
T
T
T
T
F
F
F
T
T
F
F
TSlide6
Examples
Identify the hypothesis and conclusion:
If 3x+4=-5, then
x
=-3
If you take a class in television broadcasting, then you will film a sporting event
Hypothesis: 3x+4=-5
Conclusion:
x
=-3
Hypothesis: Take a class in television broadcasting
Conclusion: Film a sporting eventSlide7
Practice
Identify the hypothesis and conclusion:
If you purchase a computer
and
don’t like it, then you can return it within 30 days.
If x+8 = 4, then
x
= - 4
Hypothesis: purchase a computer and don’t like it
Conclusion: return it within 30 days
Hypothesis: x+8=4
Conclusion:
x
= -4Slide8
Examples
Write each statement in if-then form:
Those who do not remember the past are condemned to repeat it.
Adjacent angles share a common vertex and a common side
IF you do not remember the past, THEN you are condemned to repeat it.
IF 2 angles are adjacent, THEN they share a common vertex and common side.Slide9
Practice
Write each statement in if-then form:
A polygon with four sides is a quadrilateral.
An acute angle has a measure less than 90.
IF a polygon has four sides, THEN it is a quadrilateral
IF an angle is acute, THEN its measure is less than 90.Slide10
Examples
Determine the truth vale of the following conditionals:
If a and
b
are negative, then a + b is also negative.
If you have five dollars, then you have five one-dollar bills.
T
T = T
T
F = F
Counterexample: you have 1, $5 bill.Slide11
Practice
Determine the truth vale of the following conditionals:
If two angles are supplementary, then one of the angles is acute.
If I roll two six-sided dice and sum of the numbers is 11, then one die must be a five.
T
F = F
Counterexample: 90° and 90° - neither are acute
T
T = T
5+6 = 11Slide12
FOLDABLE
INSIDE CONDITIONAL TAB
Hypothesis
If-Then Statement
ConclusionSlide13
Vocabulary
Converse-
formed by exchanging the hypothesis and conclusion
Inverse-
formed by negating the hypothesis and conclusion of the conditionalContrapositive
-
formed by negating the hypothesis and conclusion of the converse
q
p
~
p
~
q
~
q
~
pSlide14
IMPORTANT NOTE
**** NOTE:
The
conditional
and it’s contrapositive
are
logically equivalent
The
converse
and
inverse
are
logically equivalentSlide15
Examples
Write the converse, inverse, and
contrapositive
of each statement:
If 89 is divisible by 2, then 89 is an even number
If an animal is a lion, then it is a cat that can roar
Converse: If 89 is an even number, then 89 is divisible by 2.
Inverse: If 89 is not an even number, then 89 is not divisible by 2.
Contrapositive
: If 89 is not an even number, then 89 is not divisible by 2.
Converse: If an animal is a cat that can roar, then it is a lion.
Inverse: If an animal is not a lion, then it is not a cat that can roar.
Contrapositive
: If an animal is not a cat that can roar, then it is not a lion.Slide16
Examples
Write the converse, inverse, and
contrapositive
of each statement:
If you are 15 years old, then you are eligible to drive.
If the temperature is freezing, then precipitation falls as snow.
Converse: If you are eligible to drive, then you are 15 years old.
Inverse: If you are not 15 years old, then you are not eligible to drive.
Contrapositive
: If you are not eligible to drive, then you are not 15 years old.
Converse: If precipitation falls as snow, then the temperature is freezing.
Inverse: If the temperature isn’t freezing, then the precipitation does not fall as snow.
Contrapositive
: If precipitation doesn’t fall as snow, then the temperature isn’t freezing.Slide17
FOLDABLE
INSIDE CONDITIONAL TAB
Converse
Contrapositive
Inverse