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Are all physics teachers cruel
people?
| Type of statement | Statement | True or False? |
|---|---|---|
| Conditional statement | If you are in physics class, then you always have homework. | False |
| Converse statement | If you always have homework, then you are in physics class. | False |
| Inverse statement | If you are not in physics class, then you do not have homework. | False |
| Contrapositive statement | If you do not have homework, then you are not in physics class. | False |
Let's consider each of the statements one at a time using the given p and q. p =& You are in physics class q =& You always have homework
We can write the conditional statement, p→ q, in an if-then form. If you are in physics class, then you always have homework. This is not true. There will be days you do not have homework or teachers that refuse to give homework.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement. If you always have homework, then you are in physics class. Again, this is not true for the same reason the original conditional statement is not true.
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 physics class, then you do not have homework. This is not a true statement, since you could have homework in other classes.
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 don't have homework, then you are not in physics class. This is false, since you can be in physics class and not have homework. Some teachers do not like to give homework, and one of them could be a physics teacher.