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Conditional Statements
Goal: Be able to recognize conditional statements, and
to write converses of conditional statements.
If you eat your vegetables, then you will grow
up to be big and strong.
conditional statement: ___________
an if-then
______________________________
statement
hypothesis: ____________________
follows the if part
conclusion: ____________________
follows the then part
If you eat your vegetables, then you will
grow up to be big and strong.
Hypothesis: ______________________
You eat your vegetables
Conclusion: ______________________
You will grow up to be big
________________________________
and strong
If 2 lines are perpendicular, then they
form a right angle.
Hypothesis: ______________________
2 lines are perpendicular
They form a right angle
Conclusion: ______________________
Writing Conditional Statements
Ex 1: An angle of 150° is obtuse.
_____________________________________
If an angle is 150°, then it is obtuse.
Ex 2: A parallelogram has opposite sides
parallel.
If a figure is a parallelogram, then it has
_____________________________________
opposite sides parallel.
_____________________________________
A conditional can have a _____________
truth value of
true or false.
Find a counterexample where the hypothesis
is _________
and the conclusion is
true
_________.
false
Ex 3: Odd integers less than 10 are prime.
(If an odd integer is less than 10, then it is prime.)
9
Counterexample: _____________________
Ex 4: If I scored a goal, then I played soccer.
hockey
Counterexample: _____________________
Use a Venn Diagram to illustrate the
conditional statement.
Ex 5: If a food is a tomato, then it is a fruit.
fruit
tomato
converse: ____________________________
switches the hypothesis and
conclusion of a conditional statement
____________________________________
inverse: ____________________________
negates the hypothesis and
____________________________________
negates the conclusion of a conditional
____________________________________
statement
contrapositive:________________________
switches the hypothesis
and conclusion and negates both of them
____________________________________
SUMMARY OF
CONDITIONAL STATEMENTS
Conditional Statement: ________________
If p, then q. (p  q)
(p implies q)
p : ________________
hypothesis
q : _______________
conclusion
negation:____________________________________
the denial of a statement (~p is “not p”)
Converse: ________________
If q, then p. (q  p)
Inverse: ____________________________
If ~p, then ~q. (~p  ~q)
Contrapositive: _______________________
If ~q, then ~p. (~q  ~p)
Write the converse, inverse, and
contrapositive of the conditional.
If you live in Wisconsin, then you are a Packer fan.
Converse: _______________________________
If you are a Packer fan, then you live
in Wisconsin.
_______________________________________
Inverse: _______________________________
If do not live in Wisconsin, then you
are not a Packer fan.
_______________________________________
Contrapositve:____________________________
If you are not a Packer fan, then
do
not live in Wisconsin.
_________________________________________
Finding the Truth Value of a Conditional
and Converse
Ex 6: Conditional: If 2 lines do not intersect,
then they are parallel.
Converse: ___________________________
If 2 lines are parallel, then they
do
not intersect.
____________________________________
Conditional is : False
_______________________
(counterexample: skew)
Converse is : _________________________
True
Ex 7: Conditional: If a figure is a square,
then it has four right angles.
Converse: ___________________________
If a figure has four right angles,
then it is a square.
____________________________________
Conditional is : _______________________
True
Converse is : False
_________________________
(counterexample: rectangle)
Biconditionals and Definitions
Goal: Be able to write biconditionals and recognize
definitions.
Biconditional:_________________________
combined statement when
____________________________________
both
a conditional and converse are true
(join both statements with “if and only if”)
__________________________________
p if and only if q. (p <--> q)
Ex 8: Write the converse. If the converse is true,
combine the statements as a biconditional.
a.) Conditional : If three points are collinear,
then they lie on the same line. TRUE
If three points lie on the same line,
Converse:_______________________________
then they are collinear. TRUE
_______________________________________
Biconditional:____________________________
Three points are collinear if and
only if they lie on the same line.
_______________________________________
b.) Conditional : If two angles are
supplementary, then they add up to 180. TRUE
Converse: _______________________________
If two angles add up to 180, then
they are supplementary. TRUE
_______________________________________
Biconditional:____________________________
Two angles are supplementary if
and
only if they add up to 180.
_______________________________________
1
2
Writing Two Statements that Form
Biconditional
Ex 9: A whole number is a multiple of 5 if and
only if its last digit is either a 0 or a 5.
_______________________________________
If a whole number is a multiple of 5, then its
last digit is either a 0 or a 5.
_______________________________________
_______________________________________
If a whole number’s last digit is either a 0 or a 5,
then it is a multiple of 5.
_______________________________________
Note: These statements are converses
Ex 10: You like deep dish pizza if and only if you
are from Chicago.
_______________________________________
If you like deep dish pizza, then you are from
Chicago.
_______________________________________
_______________________________________
If you are from Chicago, then you like deep
dish pizza.
_______________________________________
Writing a Definition as a Biconditional
Ex 11: Test the statement to see if it is reversible.
If so, write it as a true biconditional. If not, write
not reversible.
a.) Definition: A ray that divides an angle into
two congruent angles is an angle bisector.
Conditional: _____________________________
If a ray divides an angle into two
congruent angles, then it is an angle bisector. TRUE
_______________________________________
Converse: _______________________________
If a ray is an angle bisector, then it
divides an angle into two congruent angles. TRUE
_______________________________________
Biconditional:___________________________
A ray divides an angle into two
congruent
angles if and only if it is an angle bisector.
__________________________________________
b.) Definition: A rectangle is a 4-sided figure with
at least one right angle.
Conditional: _____________________________
If a figure is a rectangle, then it is a
4-sided figure with one right angle. TRUE
_______________________________________
Converse: _______________________________
If a figure is a 4-sided figure with at
least one right angle, then it is a rectangle.
_______________________________________
FALSE, counterexample: a square
Biconditional:_______________________________
Not reversible
__________________________________________
Summary
Conditional Statement
If p, then q (p  q): ____________________________
Converse
If q, then p (q  p) : ___________________________
Inverse
If ~p, then ~q (~p  ~q): ________________________
Contrapositive
If ~q, then ~p (~q  ~p) : _______________________
p if and only if q (p <--> q) : ______________________
Biconditional