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If some Cops are Robbers, and no Robbers are Thieves, which of the following statements must be false?A. No Cops are ThievesB. Some Cops are ThievesC. Some Robbers are not CopsD. All Cops are Robbers

Question

If some Cops are Robbers, and no Robbers are Thieves, which of the following statements must be false?A. No Cops are ThievesB. Some Cops are ThievesC. Some Robbers are not CopsD. All Cops are Robbers

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Solution

The statement that must be false is B. "Some Cops are Thieves". Here's why:

  1. The first statement says "some Cops are Robbers". This means there is an overlap between Cops and Robbers.

  2. The second statement says "no Robbers are Thieves". This means there is no overlap between Robbers and Thieves.

  3. Therefore, since some Cops are also Robbers (from statement 1), and no Robbers are Thieves (from statement 2), it is impossible for any Cops to be Thieves.

So, statement B "Some Cops are Thieves" must be false.

This problem has been solved

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