Test if-then reasoning

Test if-then reasoning: guided practice

If A guarantees B, observing B does not necessarily prove A.

Use paper or a free local text editor. This is an original fictional practice case; do not submit its records to a real service. Start this lesson with these facts, even if an earlier variation changed them. Fictional club policy: if a room is booked, its calendar shows a blue block. Room B shows a blue block. Blue blocks can also mark maintenance. Room C has no blue block. Assume the rule is always followed in this exercise.

1. 1. Write the condition

   Translate the rule as booked → blue block.

   You should see: Booked rooms must show blue; the rule is one-way.

   Direction matters in conditional reasoning.

2. 2. Test B

   Ask whether maintenance could explain B’s blue block.

   You should see: B may be booked or under maintenance; booking is not established.

   Another cause of the signal blocks the reverse inference.

3. 3. Test C

   Use the absence of a required signal.

   You should see: C is not booked under the assumed rule because it has no blue block.

   If booking always creates blue, no blue rules booking out.

4. 4. Write a valid check

   Specify how to settle B’s status.

   You should see: Read B’s reservation record instead of inferring booking from color alone.

   Additional evidence can resolve what the conditional leaves unknown.