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.
Write the conditional statement in if-then
form:
The car will run if there is gas in the tank.
If there is gas in the tank, then the car
will run.
I will wake up on time if my alarm goes
off.
If my alarm goes off, then I will wake up
on time.
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!
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 you are from Mexico, then you speak
Spanish.
Inverse: If you are not from Mexico, then you do not speak
Spanish.
Contrapositive: ~q
~p
If-then statement: If you lift weights, then you will
be strong.
Contrapositive: If you are not strong, then you do
not lift weights.
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,
NJ, then you live in Monmouth County.
Converse: If you live in Monmouth County,
then you live in Red Bank, NJ.
Inverse: If you do not live in Red Bank, NJ,
then you do not live in Monmouth County.
Contrapositive: If you do not live in
Monmouth County, then you do not live in
Red Bank, NJ.