Before you take a math test you haven't studied for, you gotta ask yourself one thing — do I feel lucky?
Type of statement
Statement
True or False?
Conditional statement
If you do your math homework, then you will do well on the test.
False
Converse statement
If you do well on the test, then you did your math homework.
False
Inverse statement
If you do not do your math homework, then you will not do well on the test.
False
Contrapositive statement
If you do not do well on the test, then you did not do your math homework.
False
Practice makes perfect
Let's consider each of the statements one at a time using the given p and q.
p =& You do your math homework
q =& You will do well on the test
Conditional Statement
We can write the conditional statement, p→ q, in an if-then form.
If you do your math homework,
then you will do well on the test.
This is a false statement, as you doing your homework does not guarantee that you do well on the test. You could be unlucky and get difficult questions.
Converse
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
If you do well on the test,
then you did your math homework.
The converse of the conditional statement is also false, because you do not necessarily have to have studied to do well on the test
Inverse
The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement.
If you do not do your math homework,
then you will not do well on the test.
By the same logic we know that the conditional and converse statements are false, we know that the inverse is false.
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 do not do well on the test,
then you did not do your math homework.
Again, this is also false for the same reason why all of the other statements were false.
