Conditional Statements
How do we express and symbolize if-then
statements?
Unit 2A Day 5
Conditional statements are formed by
joining two statements with the words
if and then.
If you go to ECHS, then you are a Rebel.


The if-statement is the hypothesis.
We use the variable p to represent it.
The then-statement is the conclusion.
We use the variable q to represent it.
Example:
If you do your homework in math, then your
test grades will improve.

Hypothesis:

Conclusion:
Conditional statements can be true or false
Symbols


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The symbol →indicates a conditional
statement.
The symbol ~ negates a statement.
The symbol ↔indicates a biconditional
statement. To write a biconditional
statement in words, write “if and only if”
between the hypothesis and conclusion.
Example: Write the following statements in words and
decide whether they are true or false.
p: I have an umbrella
~ p: ________________
q: It is raining
~ q: _________________
p → q ____________________________________
q → p ____________________________________
~ p →~ q__________________________________
~ q →~ p__________________________________
p ↔ q ____________________________________
Converse: q → p
Switch the hypothesis and
conclusion
Inverse: ~ p →~ q
Negate the hypothesis and
conclusion
Contrapositive: ~ q →~ p
Biconditional: p ↔ q
Negate AND switch the hypothesis Use the words “if and only
and conclusion
if” between
1. Name the hypothesis and conclusion of the following
statement:
If a quadrilateral is a rectangle,
then it has 4 congruent angles.

Hypothesis: __________________________________

Conclusion: __________________________________
2. Name the hypothesis, conclusion, inverse, converse,
contrapositive, and biconditional.
“If the student studied, then the student made an “A”.
a.
If a student made an “A”, then the student studied.
b.
The student made an “A”.
c.
If a student did not make an “A”, then the student did not
study.
d.
A student studied if and only if the student made an “A”
e.
A student studied.
f.
If a student did not study, then the student did not make an
“A”.
3. Given p and q, write the following statements in words from
their symbolic notation. Decide whether each statement is
true or false.
p: The sun is out
a.
q: It is daytime
p → q _____________________________________
b.
q → p _____________________________________
c.
~ p →~q ____________________________________
d.
~ q →~p ____________________________________
e.
p ↔ q ______________________________________