Who Stole the Ice Cream? During an investigation into the mysterious disappearan

Question

Who Stole the Ice Cream? During an investigation into the mysterious disappearance of ice-cream from a Mr. Softee truck, the following statements were made by the prime suspects. Alan: I wouldn’t steal ice-cream unless Carl helped me. Bill: Me? Steal ice-cream? Of course not! I’m too honest for that. Besides, I hate the stuff. Carl: If I stole it then either Alan or Bill was in it too. Dave: Neither Carl nor I were involved. Given that exactly one of the four suspects is lying, and that exactly two of them were involved in the theft, determine who stole the ice-cream and who is lying. (Create Propositional Sentences based upon each suspects’ statements Followed by the Truth Table)

Symbolic Logic

Propositional Sentences based upon each suspects’ statements, the Truth Table and the justification for your conclusions

Explanation / Answer

Premise:

Alan: I wouldn’t steal ice-cream unless Carl helped me.

Bill: Me? Steal ice-cream? Of course not! I’m too honest for that. Besides, I hate the stuff.

Carl: If I stole it then either Alan or Bill was in it too.

Dave: Neither Carl nor I were involved.

Given: One of the four suspects is lying.

Exactly two of them were involved in the theft.

Bill is not involved. (B)

Carl is not involved.(D)

Dave is not involved.(D)

Bill is involved.(~B)

Carl is not involved.(D)

Dave is not inolved.(D)

Bill is not involved.(B)

Carl is not involved.(D)

Dave is not involved.(D)

Bill is not involved.(B)

Either Carl or Dave is not involved. (~D)

Therefore, we conclude that Alan and Carl are involved in stealing the ice-cream.

Alan Bill Carl Dave Comment Conclusion False True True True

Bill is not involved. (B)

Carl is not involved.(D)

Dave is not involved.(D)

3 people are not involved. This is not the case, as per given statement. True False True True

Bill is involved.(~B)

Carl is not involved.(D)

Dave is not inolved.(D)

Carl didn't helped, therefore, Alan, Carl and Dave are not involved. This is not the case, as per given statement. True True False True

Bill is not involved.(B)

Carl is not involved.(D)

Dave is not involved.(D)

Carl didn't helped, therefore, Alan, Bill, Carl and Dave are not involved. This is not the case, as per given statement. True True True False

Bill is not involved.(B)

Either Carl or Dave is not involved. (~D)

Alan, and Carl are involved.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.