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In the A Level exam you may be asked to solve simple logic puzzles like this one:

A valuable jewel was taken from a museum by one of Alice, Bob or Carl. The following facts are gathered:

1. The thief took the jewel out of the museum through the side exit
2. If Bob was in the storage room before the theft, the jewel was taken using a backpack
3. Either Bob or Carl was in the storage room before the theft occurred
4. If Carl stole the jewel, Alice was not in the lobby
5. If the jewel was put in a backpack, then Alice was in the lobby and did not steal the jewel

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Who stole the jewel?

Hint

Because most of the clues use statements like "If A, then B" (which we can write as "A implies B" or A ⇒ B), we can use the contrapositive ("not B implies not A", or B′ ⇒ A′) which is logically equivalent to the original statement. For example, for clue 4, we can use "If Alice was in the lobby, then Carl did not steal the jewel".
 

• We know from clue 1 and the contrapositive of clue 5 that Carl was not in the storage room before the theft
• We therefore know from clue 3 that Bob was in the storage room before the theft occurred
• Now from clue 2, the jewel was taken using a backpack
• From clue 5, we know that Alice was in the lobby and did not steal the jewel
• Finally, from the contrapositive of clue 4, Carl did not steal the jewel.
• The only remaining suspect is Bob, who must be the thief.

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