Warm up
Write the conditional, converse, inverse and contrapositive
statements of the following, then determine the truth value of each:
I will pick it if it’s in my nose.
Conditional:
T
If it’s in my nose, then I will pick it.
Converse:
F
If I pick it, then it’s in my nose.
Inverse
If it’s not in my nose, then I won’t pick it.
Contrapositive:
If I won’t pick it, then it’s not in my nose.
F
F
It’s homework grading time.
It’s Quiz Time
You may use your notes if they are on the
notebook you made on the first day.
Let’s add just a bit to our
notes on logic
Today, we’re going to create a definition… also
known as a biconditional statement
A Biconditional Statement
is a definition and must be true in conditional
and converse form.
p
q
Statement: Triangles are closed figures
that have three straight sides.
What is the
truth value?
True
Conditional: If it is a triangle, then it is a
closed figure with three straight sides.
What is the
truth value?
True
Converse: If it is a closed figure with
three straight sides, then it is a triangle.
Since both the conditional and converse are true, then we can write a biconditional:
It is a triangle if and only if it is a closed figure
with three straight sides.
Let’s take a closer look.
It is a triangle if and only if it is a
closed figure with three straight sides.
We do not use IF and THEN…..
We use IF AND ONLY IF…..
abbreviated as iff
It is a triangle iff it is a closed figure with
three straight sides.
Let’s work through a
couple of examples…
Statement: Two lines intersect at a point.
Conditional: If two lines intersect, they will meet at a point.
(What is the truth value?)
Converse: If two lines meet at a point, they have intersected.
(What is the truth value?)
Can we write a true biconditional?
Two lines intersect iff they meet at a point.
Statement: Big dogs burp loudly.
Conditional: If it’s a big dog, then it burps loudly.
(what’s the truth value?)
Converse: If it burps loudly, then it’s a big dog.
(what’s the truth value?)
Can we write a true biconditional?
no
Tools of the trade
Straight edge
Patty Paper
Calculator
Compass
Protractor
Please go
get one of
each