Given
If the criminal had an accomplice, then he came with the car. [1]
The criminal had no accomplice and didn’t have the key, or he had an accomplice and the key. [2]
The criminal had the key. [3]
Find
Did the criminal come with the car or not?
Solution
Definition:
A = The criminal had an accomplice.
C = The criminal came with the car.
K = The criminal had the key.
Representation:
[1]: A → C
[2]: (¬A ∧ ¬K) ∨ (A ∧ K)
[3]: K
Deduction:
[3]: K is true.
[2]: If K is true, A must be true.
[1]: If A is true, C must be true.
Answer
The criminal came with the car.