A jewelry shop has been robbed. Four suspects, A,B,C and D are rounded up for qu

Question

A jewelry shop has been robbed. Four suspects, A,B,C and D are rounded up for questioning. The detective establishes the following 4 facts: If both A and B are guilty, then C was an accomplice. If A is guilty, then at least one of B,C was an accomplice. If C is guilty, then D was an accomplice. If A is innocent then D is guilty Write these facts in symbolic form. Is it possible to establish from these facts whether A is guilty? Give a proof (=logical argument) or a counterexample (= two different assignments of guilt/innocence to A,B,C,D which do not contradict the facts, and one of them has A guilty, the other has A innocent. ) Is it possible to establish from these facts whether D is guilty? Give a proof or a counterexample.

Explanation / Answer

a,b,c,d is A,B,C,D are guilty (respectively) a) In symbolic form: a^b => c a=> b v c v d c => d ~a => d b) Counterexample: a=1 b=0 c=0 d=1 and a=0 b=0 c=0 d=1 are both valid in the given premises.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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