Quiz
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If you take a test, you can either pass or fail.
| Type of statement | Statement | True or False? |
|---|---|---|
| Conditional statement | If I take my driving test, then I will get my driver's license. | False |
| Converse statement | If I get my driver's license, then I have taken my driving test. | True |
| Inverse statement | If I do not take my driving test, then I will not get my driver's license. | True |
| Contrapositive statement | If I do not get my driver's license, then I have not taken my driving test. | False |
Let's consider each of the statements one at a time using the given p and q. p =& I will take my driving test q =& I will get my driver's license
This is false, as you could fail your driving test and thus not get your driver's license.
The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement. If I get my driver's license, then I have taken my driving test. This is true, as you need to take your driving test to get your driver's license.
The inverse of a conditional statement, ~ p→ ~ q, requires us to negate the hypothesis and the conclusion of the conditional statement. If I don't take my driving test, then I will not get my driver's license. This is a true statement, since you need to take your driving test to get your driver's license.
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 I don't get my driver's license, then I have not taken my driving test. This is false, as you could have taken your driving test and failed.