Name___________________________
Date_____________
Notes and Classwork 2.2:
Conditional Statement – logical statement with 2 parts
–
•
_________________________________
•
_________________________________
Can be written in If-then form
•
If _________________________, then _________________________________
Example – identify the hypothesis and the conclusion and write it in if-then form:
You can’t teach an old dog new tricks
If ___________________________________________________________________
Identify the hypothesis and the conclusion and rewrite it in if-then form:
•
It is time for dinner if it is 6 P.M.
–
•
There are 12 eggs if the carton is full.
–
•
If __________________________________________________________________
The measure of a straight angle is 180°
–
•
If _________________________________________________________________
If__________________________________________________________________
The car runs when there is gas in the tank.
–
If ____________________________________________________________+____
Related Conditional Statements:
–
Conditional: if p, then q
_____________________
–
Converse: if q, then p
______________________
–
Inverse: if not p, then not q
______________________
–
Contrapositive: if not q, then not p
_______________________
–
Biconditional: If p q and q  p, then it can be written as q if and only if p
(shorthand without the if’s)
________________________
1
Write in if-then form, the converse (CV), inverse (I), and the contrapositive (CP) and state whether
each is always true (AT) or not always true (NAT) - false:
•
Driving too fast often results in accidents.
 If ___________________________________________________________
 If ___________________________________________________________
CV
 If ____________________________________________________________
I
 If _____________________________________________________________ CP
•
Tourists at the Alamo are in Texas.
 If ___________________________________________________________
 If ___________________________________________________________
CV
 If ____________________________________________________________
I
 If _____________________________________________________________ CP
A biconditional is true when both p  q and q  p are true.
A biconditional ______________ is a more concise way to say (p  q)  (q  p).
Example
Create the converse and if they are both true, create the biconditional statement
“If a polygon has three sides then it is a triangle”
Converse: ______________________________________________________________
Biconditional: ____________________________________________________________
Practice – create the Converse and the Biconditional statement if the converse is true:
“If two angles are supplementary, then their sum is 180°”.
Converse: _______________________________________________________________
Biconditional: ____________________________________________________________
2
For each statement, name the relationship (converse, inverse, contrapositive) of the second
statement to the first. State whether the second is always true (AT) or not always true (NAT)
assuming pq is true.
1. If I read the book, then I can do the homework.
2. If I cannot do the homework, then I did not read the book.
1. If it is Tuesday, I go to geometry.
2. If I go to geometry, it is Tuesday
1. If it is snowing, then it is cold.
2. If it isn’t snowing, then it isn’t cold.
3