Modelling with logic: Give it a go

Be a detective

OK, now it’s your turn. Use your logic skills to solve a mystery.

Some person or people stole cookies from the cookie jar. The suspects are Albert, Betty and Clive. At least one of them committed the crime but Clive was only involved if Albert was involved and Betty would not be involved on her own.

Solve

So, who stole cookies from the cookie jar? Can you work it out?

To get you started, use the following propositions:

• Let (A) represent the proposition “Albert stole cookies from the cookie jar”.
• Let (B) represent the proposition “Betty stole cookies from the cookie jar”.
• Let (C) represent the proposition “Clive stoke cookies from the cookie jar”.

Hint

Try and model the following compound propositions:

• At least one of Albert, Betty or Clive stole cookies from the cookie jar.
• Clive stole cookies from the cookie jar only if Albert stole cookies from the cookie jar.
• If Betty stole the cookies from the cookie jar then either Albert stole cookies from the cookie jar, or Clive stole cookies from the cookie jar, or both.