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Warm Up: Follow the if
If Fred gets up before 7, then his mother
will make him breakfast. If his mother
makes him breakfast, Fred does not stop
at Bojangles. If Fred does not stop at
Bojangles then Sue has to text him about
their lunch plans. Ms. Newman has
Fred’s cell phone because he was
reading a text message in class.
What do you know? If Fred gets up at 6, what do you know?
Reasoning & Proof
Chapter 2
2.1 – Conditional Statements
2.2 – Biconditionals
Please have your week packet out to fill in notes.
Conditional

“if-then” statement.


Symbolic Form: p  q
Read as:
If p, then q.

The part after “if” is the hypothesis.

The part after “then” is the conclusion.
Ex.1:
Identifying the Hypothesis & Conclusion
Put a single underline under the hypothesis
and a double under the conclusion.
a. If you go to RHS, then you live in Durham.
b. If today is Wednesday, then tomorrow is
Thursday.
c. If y – 3 = 5, then y = 8.
Ex.2: Writing a Conditional
Write each sentence as a conditional.
a. A rectangle has 4 right angles.
b. A tiger is an animal.
c. A square has 4 congruent sides.
d. An acute angle measures less than 90 degrees.
A conditional can have a truth value of true or false.
To show a conditional true, you must show that every
time the hypothesis is true, the conclusion is true as
well—meaning you must only find a counterexample for
which the hypothesis is true, but the conclusion is false.
Ex.3: Finding a Counterexample
a.
If it is February, then there are only 28 days in the month.
b.
If you live in Jacksonville, then you live in N.C.
Ex.4: Using a Venn Diagram
Draw a Venn Diagram to illustrate this conditional.

If you live in Chicago, then
you live in Illinois.
Note: The set that makes the
hypothesis true, lies inside the set
that makes the conclusion true.
Converse

Switch the hypothesis and the conclusion.


Symbolic Form: q  p
Read as:
If q, then p.
Ex.5: Writing the Converse
Write the converse of the following conditionals.
a. If you go to RHS, then you live in Durham.
b. If two lines intersect to form right angles
then they are perpendicular.
Inverse

Put nots in front of hypothesis and
conclusion.


Symbolic Form: ~p  ~q
Read as:
If not p, then not q.
Contrapositive

Switch the hypothesis and the conclusion
and put nots in front of both


Symbolic Form: ~q  ~p
Read as:
If not q, then not p.
Ex.7: Write the inverse and the
contrapositive of the conditional.

If you go to RHS, then you live in Durham.
Inverse:
Contrapositive:
Biconditional


When a conditional and its converse are true.
“if and only if”


Symbolic form:
Read as:
p  q and q  p as p  q
p if and only if q
Ex.6: Writing a Biconditional
Consider the following conditional statements. Write the converse. If the
converse is true, combine the statement to form a biconditional.
a. If two lines intersect to form right angles, then
they are perpendicular.
Converse:
Biconditional?
b. If you are in Ms. Newman’s 3rd or 4th period
class this semester, then you are taking H.
Geometry.
Converse:
Biconditional?
Inverse



Make both the hypothesis and the
conclusion negative.
If it snows, then we will be out of
school. (p
q)
If it does not snow then we will not be
out of school. (~p
~q)
Contra-positive



Backwards and negative.
The converse of the inverse.
p
q becomes ~q
~p
My Note Page

List the logic vocabulary and the
symbols.
Cooldown
1.
What is a conditional?
2.
What is the symbolic form for contrapositive?
3.
What does  stand for?
4.
Which term goes with q  p ?