You are a famous archaeologist/treasure hunter ?a la IndianaJones. After following a treasure map you find yourself deep insidea Babylonian temple. As you reach the end of a long corridor youfind it splits into two paths. Above the first path you make outsome text carved into the rock. Shining your torch you manage tomake out the following two inscriptions on the wall:
1. L1 ? T2
2. (L1 ?T2)?(L2 ?T1)
Knowing that the Babylonians were great mathematicians, you’renot surprised to see that they had developed such a refined systemof propositional logic centuries before it should have been. Thehistorians of mathematics will surely want to hear of thisdiscovery when you’re done!
Having no idea what these variables could mean however, you lookdown at your map to see if there are any hints. You notice scrawledin the margins of the map “L1: First Path Leads to Being LostForever”, “L2: Second Path Leads to Being Lost Forever”, “T1: FirstPath Leads To Treasure” and “T2: Second Path Leads ToTreasure”.
Reading the first inscription you quickly translate the treasureis down the second path. However, as you’re about to step into thetunnel you remember something the map seller said as you wereleaving his shop: “One tells the truth and the other is a lie!” Youhad thought that was cryptic nonsense at the time but thankgoodness you remembered! He seemed like a trustworthy guy so you’llassume that his statement was true and that one inscription islying and the other is telling the truth.
Q: (20 points) Assuming the lying inscription is true and thetruthful inscription is false leads to a contradiction. Prove thisusing the laws of propositional logic. First, combine the twostatements into a single boolean expression (adding a ¬ to theexpression that you’re assuming is false). Then proceed using thelaws of propositional logic to arrive at “False”. You must showeach step and identify which law you are applying. You must use thedistributive law at least once; we are looking for you todemonstrate mastery over several laws rather than a quicksolution.
