[20pts] During a murder investigation, you have gathered the following clues:

if the knife is in the store room, then we saw it when we cleared the store room;

the murder was committed at the basement or inside the apartment;

if the murder was committed at the basement, then the knife is in the yellow dust bin;

we did not see a knife when we cleared the store room;

if the murder was committed outside the building, then we are unable to find the knife;

if the murder was committed inside the apartment, then the knife is in the store room.

We assign the following symbols to the above clues:

s : the knife is in the store room;

c : we saw the knife when we clear the store room;

b : the murder was committed at the basement;

a : murder was committed inside the apartment;

y : the knife is in the yellow dust bin;

o : the murder was committed outside the building;

u : we are unable to find the knife;

Rewrite the clues in propositional logic language and use equivalences and rules of inference to answer the question: where is the knife?. In finding the answer you should write a sequence of numbered lines, each line containing its justification in the proof (either Clue or else one of the rules of inference or equivalence laws). If the rule used has no name, then you should describe it as best you can.