Download 2.2 Analyzing Conditional Statements

2.2 Analyzing Conditional
Statements
Conditional Statements:
are statements that can be put in “In-Then” form
“If-Then” Form: If A (Hypothesis), then B (Conclusion)
Ex. Conditional Statement:
“All birds have feathers.”
Hypothesis (A)
Conclusion (B)
Conditional Statement (In “If-Then” form):
“If it is a bird, then it has feathers.”
Hypothesis (A)
Conclusion (B)
On your own…
Rewrite the conditional statements in if-then form:
“All vertebrates have a backbone”
“All triangles have 3 sides”
2
“When x=2, x =4
Negation
A statement that is the opposite of the original
“Guitar players are musicians.”
Hypothesis (A)
Conclusion (B)
Related Conditionals
T/F
T/F
Decide
whether
each
statement
If it is
Decide whether
each
statement
is true is
or true
false.orIf false.
it is
false,
give
a counterexample.
false, give
a counterexample.
T
__
Conditional (If-then) If A, then B
If someone is a guitar player, then they are a musician
F
__
Converse
If B, then A
If someone is a musician, then they are a guitar player
F
__
Inverse
If not A, then not B
If someone is not a guitar player, then they are not a musician
T
__
Contrapositive
If not B, then not A
If someone is not a musician, then they are not a guitar player
Conditional Statement: “If two angles form
a linear pair, then they are supplementary.”
T/F
Decide whether each statement is true or false. If it is false, give a
counterexample.
__
T
Conditional (If-then)
“If two angles form a linear pair, then they are supplementary.”
__
F
Converse
“If two angles are supplementary, then they form a linear pair.”
__
F
Inverse
“If two angles do not form a linear pair, then they are not supplementary.”
__
T
Contrapositive
“If two angles are not supplementary, then they do not form a linear pair.”
TRY ON YOUR OWN
Conditional Statement: “If a dog is a Great Dane, then it is
large.”
T/F
Write the converse, the inverse, and the contrapositive of the
conditional statement. Tell whether each statement is true or false.
If it is false, give a counterexample.
T
__
Conditional (If-then)
“If a dog is a Great Dane, then it is large.”
F
__
Converse
“If a dog is a large, then it is a great Dane.”
F
__
Inverse
“If a dog is not a Great Dane, then it is not large.”
T
__
Contrapositive
“If a dog is not large, then it is not a Great Dane.”
FALSE
Conditional Statement: “All
equilateral polygons are regular”
T/F
Decide whether each statement is true or false. If it is false, give a
counterexample.
F
__
Conditional (If-then)
“If a polygon is equilateral, then the polygon is regular.”
__
T
Converse
“If a polygon is regular, then the polygon is equilateral.“
T
__
Inverse
“If a polygon is not equilateral, then the polygon is not regular.”.”
F
__
Contrapositive
“If a polygon is not regular, then the polygon is not equilateral.“
Biconditional Statement
-
-
a statement that contain the phrase
“if and only if”
Used when both the conditional
statement and it’s converse are true
Ex:
Definition: If two lines intersect to form a right angle,
then they are perpendicular
Converse: If two lines are perpendicular, then they
intersect to form a right angle
Biconditional: Two lines are perpendicular if and only if
they intersect to form a right angle
Biconditional Statement
On your own…
If Mary is in the theater class, then she will
be in the fall play.
If she is in the fall play, then she must be in
the fall play.