Sec 2-2
Concept: Analyzing Conditional Statements
Objective: Given a conditional statement, identify the
hypothesis and conclusion, then be able to write the
converse, negation, inverse and contrapositive and
biconditional as measured by s.g.
Example 1: rewrite the conditional
statement in if-then form
 All
sharks have a boneless skeleton
If a fish is a shark, then it has a
boneless skeleton
Can You? Identify the
Hypothesis and Conclusion of
the conditional statement
Example 2: Rewrite the conditional
statement in if-then form
 All
cows eat grass
If an animal is a cow, then it eats
grass
Can you? Write the
converse, inverse
and contrapositive?
Example 2 Continued: Now Write the
converse, inverse and contrapositive
All cows eat grass
Conditional: If an animal is a cow, then it eats grass
Converse: if an animal eats grass, then it is a cow.
Inverse: If an animal is not a cow, then it does not eat grass
Contrapositive: If an animal does not eat grass, then it is
not a cow
Example 3: write the converse, inverse and contrapositive.
Tell whether each statement is true or false.
If a dog is a Great Dane, then it is large.
Example 4:
Winds At Sea: Use the portion of the Beaufort wind
scale table shown to determine whether the biconditional statement is
true or false. If false, provide a counterexample.
A. A storm is a hurricane if
and only if the winds of the
storm measure 64 knots or
greater.
Beaufort Wind Scale for Open Sea
Number
Knots
Description
8
34-40
Gale winds
9
41-47
Strong Gale
10
48-55
Storm
11
56-63
Violent Storm
12
64+
Hurricane
TRUE
To be true both the
conditional and
converse must be true.
Conditional: If a storm is a hurricane, then the winds of the storm
measure 64 knots or greater.
Converse: If the winds of the storm measure 64 knots or greater, then
the storm is a hurricane.
Example 4 cont.:
Winds At Sea: Use the portion of the Beaufort
wind scale table shown to determine whether the biconditional statement
is true or false. If false, provide a counterexample.
B. Winds at sea are
classified as a strong gale if
and only if the winds
measure 34-40 knots
To be true both the
conditional and
converse must be true.
Beaufort Wind Scale for Open Sea
Number
Knots
Description
8
34-40
Gale winds
9
41-47
Strong Gale
10
48-55
Storm
11
56-63
Violent Storm
12
64+
Hurricane
Conditional: If a winds at sea are a strong gale, then the winds
measure 34-40 knots.
Counterexample: Winds of 41-47 are strong gale
Example 5: Rewrite the true statement in if-then form and write the converse. If
the converse is true, combine it with the if-then statement to form a true
biconditional statement. If the converse is false provide a counter example.
Adjacent angles share a common side
If-then: If 2 angles are adjacent, then they
share a common side.
Converse: If 2 angles share a common
side, then they are adjacent.
Biconditional: 2 angles are adjacent if and
only if they share a common side.
Note: The biconditional becomes a definition
Example 6: Determine whether the biconditional statement about
the diagram is true or false. IF false provide a counter example.
SR is perpendicular to QR if and only if
<SRQ measures 90°
P
TRUE
Q
Write the conditional and
converse and determine
if they are both true.
S
Conditional: If SR is Perpendicular to QR, then <SRQ
measures 90°
Converse: If <SRQ measures 90°, then SR is
Perpendicular to QR.
R
Today’s Work
In Class:
HW:.