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Section 2.2
Analyze Conditional
Statements
What is an if-then statement?
If-then statements can be used to clarify
statements that may seem confusing.
These statements are logic statements.
Logic statements are important in many
different types of professions.
Examples:
1.
2.
3.
If the sun shines, then the grass will
grow.
If I live in NJ, then I live on the east
coast.
If the month is January, then next month
is February.
These if-then statements are called conditional
statements or conditionals.
Conditional Statement: A logical statement that
has two parts.
In general, these conditionals are written:
If p, then q
or
p
q.
Where p is the hypothesis and
q is the conclusion.
Let’s take a look back at our
examples:
1.
2.
3.
If the sun shines, then the grass will
grow.
If I live in NJ, then I live on the east
coast.
If the month is January, then next
month is February.
Converse: Exchange the hypothesis and
conclusion of the conditional.
The converse of p
q is q
p.
Conditional: If I live in NJ, then I live on the
east coast. True!
Converse: If I live on the east coast, then I live
in NJ. False!
Write the converse of the following
statement and decide if it is true or false:
Conditional: If two angles are adjacent, then
they have a common side.
Converse: If two angles have a common
side, then they are adjacent. FALSE!!
 CAD and  BAD
B
share a common side,
but they are not
adjacent angles.
C
A
D
The denial of a statement is called a
negation.
~p represents “not p”
3.) This is geometry.
1.) An angle is
This is not
obtuse.
geometry.
An angle is not
4.) Today is not
obtuse.
Thursday.
2.) A puppy is a dog.
A puppy is not a Today is Thursday.
dog.
The inverse of a conditional can be formed
by negating both the hypothesis and
conclusion.
~p
~q
If-then Statement: If two angles are vertical, then they are
congruent.
Inverse: If two angles are not vertical, then they are not
congruent.
50º
50º
These are
congruent, but not
vertical. The
inverse is FALSE!
Contrapositive: can be formed by negating
the hypothesis and conclusion of the
converse of the given conditional.
Whoa! What does that mean????!!!
~q
~p
If-then statement: If two angles are vertical, then they
are congruent.
Contrapositive: If two angles are not congruent, then
they are not vertical.
Is the contrapositive of this statement true or false???
Quick Review
If-then statement: If p, then q.
Converse: If q, then p.
Inverse: If ~p, then ~q.
Contrapositive: If ~q, then ~p.
Let’s put it all together!
If-then statement: If you live in Red Bank,
then you live in New Jersey.
Converse: If you live in New Jersey, then
you live in Red Bank.
Inverse: If you do not live in Red Bank, then
you do not live in New Jersey.
Contrapositive: If you do not live in New
Jersey, then you do not live in Red Bank.
Equivalent Statements

A conditional statement and its contrapositive
are either both true or false.

The converse and inverse are either both true or
both false.

When two statements are both true or both false,
they are called equivalent statements.
Biconditional Statements

When a conditional statement and its
converse are both true, you can write them
as a biconditional statement.

Biconditional Statement: A statement that
contains the phrase “if and only if”.
Rewrite as Biconditional
Statements
1.) Rewrite the definition of right angle as a
biconditional statement.
An angle is a right angle if and only if the
measure of the angle is 90 degrees.