Problem 1. (30 points)
a) (10 points) August and Ajay are playing basketball at the FitRec. After diving for a loose ball,
Ajay rolled his ankle! Out of spite after getting his umbrella stolen (see lab 1), August gives the
following convoluted directions to first aid.
• 'You should go to the second floor and, if you must go right from the courts, then you must
go to the third floor.'
• 'You should not go left or you must go right.'
Ajay, a capable logician, knows that the information will definitely help him find first aid. Let's
start by translating each of August's directions into propositional logic. Let:
• l denote Ajay must go left from the courts
• r denote Ajay must go right from the courts
• s denote Ajay must go to the second floor
• q denote Ajay must go to the third floor
b) (5 points) August then adds that either statement could be true, or both. Modify your translated
statement to reflect this.
c) (10 points) Ajay knows that he can transform the proposition into a simpler set of instructions.
Use the laws of equivalence to show that the proposition you've made is equivalent to $r \lor s \lor \neg l$.
d) (5 points) August then admits that he lied, meaning the proposition you made was false! How
can Ajay use this fact to find first aid? Where is first aid located?
Hint: First aid is either left or right of the courts, but not both. It also is either
second or third floor, but not both.
