Concept explainers
Exercises 57 and 58 refer to the chapter opener on page 83 Humphrey the hero deduced from the rid- die that there are twin trolls who take shifts guarding the magicaldoors One of them tells only truths, the other only lies When the troll standing guard sees Humphrey, he says
‘If truly Truthful Troll I be then go thou east and be thou free "
Humphrey needs to decide which troll he is addressing, call him by name, and tell him which door he would like opened
There are two things Humphrey must get right the name of the troll and the proper door if he misidentifies the troll, no door will be opened if he correctly names the troll and
picks the wrong door, ne will be confined to the dungeon behind it
57 3Because the troll either always lies or always tells the truth Humphrey knows that
1 if the troll is Truthful Troll then the conditional statement he uttered is true and
2 if the conditional statement he uttered is true, then he is Truthful Troll
Let p represent ‘the troll is Truthful Troll* and let q represent ‘the door to the east leads to freedom " Express the statements in (1) and (2) in symbolic form58 The conjunction of the answers from Exercise 57 is a biconditional that must be true
a Build a truth table for this biconditional.
b Use the fact that it must be true to solve Humphrey's riddle
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