Question

Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child if Carl is not her youngest child. Write down a knowledge base that describes this riddle and the necessary background knowledge that only one of the three children can be her youngest child. Show with resolution that Bill is her youngest child.

Answer 1

This popular puzzle can be represented as A ∨ B ∨ C  and if Bill is her youngest child the resolution is B = ¬A ∨ ¬C

Most situations including some puzzles can be represented using logic symbols and relating the statements involved. Let's represent this puzzle.

There are three children: Alice, Bill, and Carl, they can be represented as A, B, C

The puzzle says only one of them is the youngest, this can be represented as:

• A ∨ B ∨ C  ( V means "or")

Also, if Alice is the youngest then Bill is not the youngest

• A = ¬B (¬ is used for negation)

Similarly is Alice is not the youngest Carl is not the youngest can be represented as

• ¬A = ¬C

Finally, if Bill is the youngest we can say

B = ¬A ∨ ¬C ( Billie  is the youngest because Alice and Carl are not the youngest)

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