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 magical doors. 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 or me troll and the proper door, If he misidentifies the troll, no door will be opened. If he correctly names the troll and picks me wrong door, he win be confined to the dungeon behind it.
Because 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 form.
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Mathematical Ideas (13th Edition) - Standalone book
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