Geometry Honors
Section 2.2
Introduction to Logic
Complete the Venn diagram to represent
the statement
“All whales are mammals”.
mammals
whales
Venn diagrams are also called
______
Euler diagrams,
after the Swiss mathematician
____________.
Leonard Euler
You should be able to see from the
diagram that the following
statement is true.
(1) If an animal is a whale, then it is
a mammal.
If-then statements like statement
(1) are called *___________
conditionals.
In a conditional statement, the
phrase following the word “if” is
hypothesis The phrase
the *_________.
following the word “then” is the
*_________.
conclusion
If you interchange the hypothesis
and the conclusion of a
conditional, you get the *converse
of the original conditional.
Example: Write a conditional with the
hypothesis “an animal is a reptile” and the
conclusion “the animal is a snake”.
If an animal is a reptile than it is a
snake.
True or false? False
What is a counterexample?
crocodile
Write the converse of the conditional.
If an animal is a snake, then it is
a reptile.
True or false? True
Consider the following statements:
If a car is a corvette, then it is a Chevrolet.
Susan’s car is a corvette.
Complete the Euler diagram including an * to
represent Susan’s car.
chevrolet
corvette

Does this mean that Susan’s car is a Chevrolet?
yes
Conditionals can be linked together
to form logic chains.
(It does not matter whether the
conditionals are true.)
Example: Consider the following conditionals.
If cats freak, then mice frisk.
If sirens shriek, then dogs howl.
If dogs howl, then cats freak.
Prove the conditional “If sirens shriek, then mice
frisk.” follows from the 3 given conditionals by
arranging the 3 conditionals in the proper order.
If sirens shriek, then dogs howl.
If dogs howl, then cats freak.
If cats freak, then mice frisk