If it is not Valentine's Day, then it is not February.
False
Contrapositive statement
If it is not February, then it is not Valentine's Day.
True
Practice makes perfect
Let's consider each of the statements one at a time using the given p and q.
p &= It is Valentine's Day
q &= It is February
Conditional Statement
We can write the conditional statement, p→ q, in an if-then form.
If it is Valentine's Day,
then it is February.
Since Valentine's Day is on the 28th of February, the conditional statement is true.
Converse
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
If it is February,
then it is Valentine's Day.
This is not true as there are 27 other days in February that are not Valentine's Day.
Inverse
The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement.
If it is not Valentine's Day,
then it is not February.
Again, there are 27 other days in February that are not Valentine's Day. Therefore, if it is not Valentine's Day it could still be February. This statement is therefore 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 it is not February,
then it is not Valentine's Day.
This is a true statement. If the month is not February, it cannot be Valentine's Day.
