Transcript Conditional Statements

C ONDITIONAL S TATEMENTS
PARTNER C HALLENGE
Amy, Bob and Carla are in a band. One is
the drummer, one is the guitarist, and one
is the keyboard player. Use the clues to
find the instrument that each plays.
Instrument
Drums
Guitar
Keyboard
Amy
Bob
Carla
PARTNER C HALLENGE
Instrument
Amy
Bob Carla
Drums
Guitar
Keyboard
•Carla and the drummer wear differentcolored shirts.
•The keyboard player is older than Bob.
•Amy, the youngest band member, lives next
door to the guitarist.
Vocabulary
Conditional Statement – an if-then
statement
Example:
If you are not completely satisfied, then
your money will be refunded.
Vocabulary
hypothesis– the part of the conditional
statement following “if”.
Example:
If you are not completely satisfied,
then your money will be refunded.
Vocabulary
conclusion– the part of the conditional
statement following “then”.
Example:
If you are not completely satisfied, then
your money will be refunded.
Your Turn:
Identify the hypothesis and the conclusion
of the following conditional statement.
If y – 3 = 5, then y = 8.
Your Turn:
Write the following sentence as a
conditional statement.
An integer that ends with a zero
is divisible by 5.
Your Turn:
Write the following sentence as a
conditional statement.
A square had four congruent
sides.
Vocabulary
Truth value– determining if the
conditional statement is TRUE or FALSE.
A conditional statement is TRUE if every
time the hypothesis is true, the conclusion
is also true.
Example of a true conditional statement:
If a figure is a square, then it has four
congruent sides.
Vocabulary
Truth value– determining if the
conditional statement is TRUE or FALSE.
A conditional statement is FALSE if you
can find just one counterexample for
which the hypothesis is true and the
conclusion is false.
Example of a false conditional statement:
If you go to Wallenpaupack Area HS, then
you live in Hawley, PA.
Your Turn:
Determine the truth value of the following
conditional statement.
If you live in Philadelphia, then
you live in Pennsylvania.
Your Turn:
Determine the truth value of the following
conditional statement.
If a quadrilateral has four right
angles, then the quadrilateral is a
square.
Vocabulary
Venn Diagram– a diagram made up of
overlapping circles/ovals.
A Venn Diagram can be useful in
determining the truth value of a
conditional statement.
Venn Diagram to represent a
TRUE conditional statement.
If you are legally driving, then you are at
least 16 years old.
Legal Drivers
16 year olds
Venn Diagram to represent a
FALSE conditional statement.
If you play the flute, then you are in the
band.
Flute
Players
Band
Members
Vocabulary
Converse of a Conditional Statement–
switch the hypothesis and the conclusion.
Example:
Conditional Statement:
If 2 lines are not parallel and do not
intersect, then they are skew.
Converse:
If 2 lines are skew, then they are not
parallel and do not intersect.
Conditional Statement:
If 2 lines are not parallel and do not
intersect, then they are skew.
True or False
Converse:
If 2 lines are skew, then they are not
parallel and do not intersect.
True or False
Conditional Statement:
If a figure is a square, then it has four
sides.
True or False
Converse:
If a figure has four sides, then it is a
square.
True or False
Symbolic Form
Conditional Statement– if p, then q.
pq
Converse– if q, then p.
qp
H OMEWORK
pg. 71: 1-31 odd,
43-48, 54-58.
Logic and Sudoku
Vocabulary
Biconditional Statement – a statement you
get by connecting the conditional
statement and its converse with the word
“and”.
You can also use the phrase “if and only if”.
Can only be combined if the conditional
statement and its converse are both true.
Example of a Biconditional:
Conditional Statement:
If two angles have the same measure,
then the angles are congruent.
Converse:
If two angles are congruent, then the
angles have the same measure.
Since both the conditional and converse
statements are true…
Biconditional:
Two angles have the same measure if and
only if the two angles are congruent.
Symbolic Form
Conditional Statement– if p, then q.
pq
Converse– if q, then p.
qp
Biconditional– p if and only if q
pq
What makes a Good Definition?
Uses clearly understood terms
Precise (don’t use words such as sort of,
or some)
Reversible (can be written as a
biconditional)
Is this a Good Definition?
A right angle is an angle whose measure is
90.
Good Definition
Conditional: If an angle is a right angle,
then it measures 90.
Converse: If an angle measures 90, then it
is a right angle.
Biconditional: An angle is a right angle if
and only if its measure is 90.
Is this a Good Definition?
An airplane is a vehicle that flies.
 Bad Definition 
Conditional: If its an airplane, then it’s a
vehicle that flies.
Converse: If it’s a vehicle that flies, then it
is an airplane.
Counterexample: A helicopter is a vehicle
that flies.
H OMEWORK
pg. 78: 1-23, 27,
32-35.
PARTNER C HALLENGE
Alan, Ben, and Cal are seated as shown with their eyes
closed. Diane places a hat on each of their heads from
a box that contains 3 red hats and 2 blue hats. They
open their eyes and look forward. Alan says, “I cannot
deduce what color hat I’m wearing.” Hearing that, Ben
says, “I cannot deduce what color hat I’m wearing
either.” Cal then says, “I know what color I am
wearing.” What color is Cal’s hat? How does Cal know
the color of his hat?
Alan
Ben
Cal
Vocabulary
Negation– having the opposite truth
value.
Example of Negation:
Statement: I studied 4 hours.
Negation: I did not study 4 hours.
Statement: I do not like reading books.
Negation: I like reading books.
Symbolic Form
~
Vocabulary
Inverse of a Conditional Statement–
negation of both the hypothesis and the
conclusion.
Conditional Statement:
If two angles have the same measure,
then the angles are congruent.
Inverse:
If two angles are not congruent, then the
angles do not have the same measure.
Vocabulary
Contrapositive of a Conditional Statement–
switches the hypothesis and the conclusion
and negates both.
Conditional Statement:
If a figure is a square, then it is a rectangle.
Contrapositive:
If a figure is not a rectangle, then it is not a
square.
Switch and negate both
Symbolic Form
Conditional Statement– if p, then q.
pq
Negation– not p
~p
Inverse– If not p, then not q
~p  ~q
Contrapositive– If not q, then not p
~q  ~p
Conditional Statement
pq
If a person is old enough to vote,
then he/she is at least 18 years old.
Converse
qp
If a person is at least 18 years old, then
he/she is old enough to vote.
~p  ~q
Inverse
If a person is NOT old enough to vote, then
he/she is NOT at least 18 years old.
Contrapositive ~q  ~p
If a person is at NOT least 18 years old, then
he/she is NOT old enough to vote.
Biconditional Statement
A person is old enough to vote, if
and only if he/she is at least 18
years old.
H OMEWORK
pg. 267: 1-9, 2227, 33-35, 42-44
Logic and Sudoku
2 9
3
7
6
4
9
7
1 5
3
8 9
1
6 8
3
7 4
5 3
9
7 6
4
1
6
9 2
1 4
5
1 8
1 5
3
8 4 9
5
9 6
2 7 4
2
3 8
3 7 4 1
8
6
2 9
Possible Hat Combinations:
Alan Ben
If Benwould
saw blue,
hewhat
new
Alan
know
that
he wearing
was wearing
he
was
if he red.
saw
Therefore,
he did
not see
two
blue hats
in front
of
blue.
him.
Therefore, Cal must be
wearing red.
R
R
R
R
B
B
B
R
R
B
B
R
R
B
Cal
R
B
R
B
R
B
R