The famous detective Percule Hoirot was called in to solve a baffling murder mystery. He determined the following facts:

1. Lord Hazelton was killed by a blow on the head with a brass candlestick, not a fatal dose of strychnine.

2. Either Lady Hazelton or a maid, Sara, was in the dining room at the time of the murder.

3. If the cook was in the kitchen at the time of the murder, then the butler killed Lord Hazelton with a fatal dose of strychnine.

4. If Lady Hazelton was in the dining room at the time of the murder, then the chauffeur killed Lord Hazelton.

5. If the cook was not in the kitchen at the time of the murder, then Sara was not in the dining room when the murder was committed.

6. If Sara was in the dining room at the time the murder was committed, then the wine steward killed Lord Hazelton. Solve the mystery by determining who murdered Lord Hazelton.

Translate statements 1-6 and your conclusion into formal logical forms and give formal proof of your answer using the logical equivalences and rules of inference.

Convert 101110102 from binary to decimal.