If you are in math class, then you are in geometry.
False
Converse statement
If you are in geometry, then you are in math class.
True
Inverse statement
If you are not in math class, then you are not in geometry.
True
Contrapositive statement
If you are not in geometry, then you are not in math class.
False
Practice makes perfect
Let's consider each of the statements one at a time using the given p and q.
p =& You are in math class
q =& You are in geometry
Conditional Statement
We can write the conditional statement, p→ q, in an if-then form.
If you are in math class,
then you are in geometry.
This is not necessarily true as math is much more then geometry. You could for example be in a fun algebra class. Therefore, the conditional statement is false.
Converse
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
If you are in geometry,
then you are in math class.
The converse of the conditional statement is true, since geometry is math.
Inverse
The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement.
If you are not in math class,
then you are not in geometry.
This is a true statement, as if you are not in math class you are not studying anything math related, including geometry.
Contrapositive
The contrapositive of a conditional statement, ~ q→ ~ p, starts out with the converse of the conditional statement. Then we have to negate the hypothesis and the conclusion.
If you are not in geometry,
then you are not in math class.
By the same logic used to know that the conditional statement was false, we know that the contrapositive is false. Again, math is not only geometry. If you are not in geometry, you could be in a trigonometry class, which is also math.
