Soru
Draw a set diagram to determine whether the conclusion follows logically from the premises. If you are the ninth caller, then you win a free ticket. You are not the ninth caller. Therefore, you did not win a free ticket. Valid argument Invalid argument If you have the flu , then you need to stay home. You need to stay home. Therefore, you have the flu. Valid argument Invalid argument
Çözüm
4.4
(176 Oylar)
Behçet
Elit · 8 yıl öğretmeni
Uzman doğrulaması
Cevap
To determine whether the conclusions follow logically from the premises, we can analyze each argument using logical reasoning and set diagrams.### Argument 1:**Premises:**1. If you are the ninth caller, then you win a free ticket.2. You are not the ninth caller.**Conclusion:**- Therefore, you did not win a free ticket.**Analysis:**This argument follows the form of "If P, then Q. Not P. Therefore, not Q." This is known as denying the antecedent, which is a formal fallacy in logic. Just because you are not the ninth caller does not necessarily mean you cannot win a free ticket through other means.**Set Diagram:**- Let Set A represent people who are the ninth caller.- Let Set B represent people who win a free ticket.- The premise states that Set A is a subset of Set B.- However, being outside Set A (not the ninth caller) does not imply being outside Set B (not winning a free ticket).**Conclusion:**- **Invalid argument**### Argument 2:**Premises:**1. If you have the flu, then you need to stay home.2. You need to stay home.**Conclusion:**- Therefore, you have the flu.**Analysis:**This argument follows the form of "If P, then Q. Q. Therefore, P." This is known as affirming the consequent, which is also a formal fallacy in logic. Needing to stay home could be due to reasons other than having the flu.**Set Diagram:**- Let Set C represent people who have the flu.- Let Set D represent people who need to stay home.- The premise states that Set C is a subset of Set D.- Being in Set D (needing to stay home) does not necessarily mean being in Set C (having the flu).**Conclusion:**- **Invalid argument**In both cases, the arguments are invalid because they commit logical fallacies.