Daily Logic Puzzle
P1.
If it rains today, then the ground will be wet.
P2.
If the ground is wet, then the outdoor event will be cancelled.
P3.
The outdoor event was not cancelled.
Q.
What can we logically conclude about whether it rained today?
Working Space
Solution
Step 1: From P1, we know: R → W (Rain implies Wet).
Step 2: From P2, we know: W → C (Wet implies Cancelled).
Step 3: By hypothetical syllogism: R → C (Rain implies Cancelled).
Step 4: From P3, we know: ¬C (Not Cancelled).
Step 5: By modus tollens on R → C and ¬C: ¬R (It did not rain).
Therefore, we can logically conclude that it did not rain today.
Rules used: Hypothetical Syllogism, Modus Tollens