Think & Click: Converse and Biconditional Statements
Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.
Determine the converse of each statement, and then decide if it could appropriately be written as a biconditional statement:
If I burn the popcorn, then the kitchen will smell bad.
Converse: If the kitchen smells bad, then I burned the popcorn.
No, it can’t be appropriately written as a biconditional statement. Though it may smell bad because of the popcorn, there are other reasons that the kitchen could smell bad. The converse is not always true.
Converse: If an angle measures more than 90 degrees, then it is obtuse.
No, it can’t be appropriately written as a biconditional statement. It may be obtuse, but it could also be a reflex angle. Note: If the original statement had read, "If an angle is obtuse, then it measures between 90 and 180 degrees," then a biconditional statement would have been appropriate.
If a number is prime, then its only factors are 1 and itself.
Converse: If a number’s only factors are 1 and itself, then it is prime.
Yes, it can be appropriately written as a biconditional statement. This is the definition of prime numbers.
