Logic+2

Sorry everyone! I thought I'd put this page up....here it is now! :) As always, due by midnight on Sunday!

I found some cool logic problems...let's tackle a couple--- Chew on this...

TRUE STATEMENTS:

A. The number of false statements here is one.

B. The number of false statements here is two.

C. The number of false statements here is three.

D. The number of false statements here is four.

Which of the above statements is true?

Here's the solution: The answer is "C": Three statements are false. Since each statement concludes that there is a different number of false statements, that proves that only one statement can be correct (hence the object is to decide which statement is true). Given that one statement is true, by definition, the other three must be false!

Melissa and Jessica were working on the computer along with their friends Sandy and Nicole. Suddenly, I heard a crash and then lots of shouts. I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass! Sandy and Jessica spoke almost at the same time:

Jessica saying, "It wasn't me!" Sandy saying, "It was Nicole!" Melissa yelled, "No, it was Sandy!" With a pretty straight face Nicole said, "Sandy's a liar."

Only one of them was telling the truth, so who knocked over the monitor?

Here's the solution: Nicole was telling the truth; Jessica broke the monitor.

If only 1 of the 4 was telling the truth, that means that 3 were not telling the truth. Using deductive reasoning, one would conclude that the only possibility with the presented facts is that Jessica was lying when she said, "It wasn't me," Sandy was lying when she said, "It was Nicole," and Melissa also lied when she said, "No, it was Sandy." This leaves Nicole as the truth-teller, revealing Jessica as the culprit, having stated as a direct lie when she said,"It wasn't me!"

After you've figured them out, talk about how logic affected your capacity to reach that "conclusion," and what kind of knowledge does this become for us?

E.Tenort: Okay the red one is the easy one; the one telling the truth is Nicole because her statement is true even it the incident did not happen. All humans lie; Sandy is a human; therefore Sandy is a liar. That simple syllogism makes Nicole's statement as true no matter whose fault it is. Not to say that humans can not tell the truth and Sandy might be telling the truth, but based of the information given we can logically conclude that Nicole tells the truth.Knowing this all other claims are lies including Jessica's so we can conclude it was her.

J.Olivas: I find the problem in red to be more interesting than the one in blue since it seems like a real life scenario(as it probably is intended to be seen as). To know the truth here, as in many cases, one must speculate because one was not there. To begin, trying to figure out what happened we must take into account that the person most likely to lie would be the person who actually knocked over the monitor because telling the truth would not benefit the as much as getting out of the problem would. And although, it may be a fallacious assumption it seems to be necessary in order to figure out who knocked the monitor. Second of all there is the clarity with which the group blames Sandy. Melissa flat-out blames Sandy for the deed, Nicole(with a pretty straight face) denies that she knocked over the monitor by calling Sandy a liar, and Jessica simply she did not do it. Because of the testimonies of the girls I can conclude that Sandy was the most likely culprit. However, this conclusion is not without it's downfalls such as the possibility that Jessica, Melissa and Nicole all had some sort of grudge against Sandy which led to them blaming Sandy for knocking over the monitor. The conclusion also doesn't take into account the possibility that the monitor simply fell because of a prior misplacement upon its foundation and none of the girls actually knocked it down.

E.Tenort: C. is true it can not be A because that means more then one statement is true and that can not be they would conflict. It can not be B for the same reason. It cannot be D because that would make all statements wrong including itself.

L.Silva: I agree with Mr. Tenort. Answer C would eliminate three answer, which would have to be A, B and D to make C the only true answer.

A.Castaneda: I am assuming that the one guilty for the monitor to fall was Nicole because of the denial; and I believe that one saying the truth is Jessica because she didn't blame the accident on no one else, but immediately cleared her name from the accident. As to the part in blue I as well agree that the correct answer is C.

M.Gutierrez: I think that you cant actually know 100% who broke the monitor because any one of them could be lying, even Nicole could have broken it. Just because she has a straight face does not mean she is telling the truth. I also agree that the correct answer is C.

M.Agundez: I agree with Mr.Gutierrez because there are some people who are very good liars so we cannot just take Nicole off the guilt list. The one who most likely did not do it would be Jessica because she just cleared her name instead of blaming another.

M.Gutierrez: I have to say that Melissa is the one that broke the monitor because if only one of them is telling the truth you have to assume who is the one telling the truth. Jessica is out of the picture because nobody is accusing her of anything and she is the one that clearly said that it wasn't her that broke the monitor so we have to assume that she is telling the truth. And then it couldn't be Sandy because if everybody else is lying then that would mean that Sandy is innocent. And if everybody else is lying then that would mean that Sandy is lying too so that means it wasn't Nicole either so it had to be Melissa

L. Silva: It couldn't be Melissa telling the truth because otherwise that would make Nicole's statement true as well, which is not possible. The same type of reasoning applies to Nicole's statement, beacause that would make Melissa's statement true as well. Sandy's statement would make both Nicole's and Melissa's statement false, although not Jessica's necessarily. Thus, Jessica is the only one telling the truth because her statemnt does not contradict with any of the other girl's statements, making the girl's statements possibly true but since we have proven their statements wrong, it is only safe to say Jessica is the one telling the truth. I believe the guilty person is left ambiguous.

M.Agundez: Mr.Silva just because Nicole says that Sandy is a liar does not make Melissa's statement true as well she is simply just clearing her name by attacking Sandy's claim.

E.Gutierrez: I agree with the majority of commentators that state C as the only true statement. The second situation is much more interesting because it often takes place in real life, just not in exactly the same way. Many judges often sentenced innocent people to years in prison for crimes they did not commit before forensic science was used in the criminal justice system. Mr.Olivas' point that Melissa and Nicole both had a grudge against Sandy is perfectly valid;however, i believe the monitor fell because of some sort of misconduct on Sandy's part.

N.Cuevas: The most logical answer for who broke the monitor would be jessica since the other girls are arguing and blaming each other and we will never know who it was. However, Jesiica only affirms that she never broke the monitor without blaming the others. At fisrt, I thought that Sandy broke the monitor but after analysing it, i came with the conclusion that the only person saying the truth was Jessica.

N.Cuevas: I could not understand the blue problem. Can someone explain why it is C?

L. Silva: Ms. Cuevas, you should look at Mr. Tenort's explanation of the blue problem. He does a very good job at breaking it down by using logic.

J.Olivas: Of course logic has it's great advantages but as with any system it is not perfect. Take for example the following sentence: "This statement is false." How do we apply logic to figure out the validity of that?!

E.Gutierrez: Ms.Cuevas, if you think Jessica is the one who broke the monitor, than how can she be telling the truth by saying that she didn't break the monitor?

G.Yanez: Very well Tenort, you have a very coherent explanation for the problem in blue.

G.Yanez: The only one who is not being blamed by anyone is Jessica, however, she is just saying that it was not her who knocked over the monitor. The other girls are just blaming one another. Therefore, we cannot know with certainty who knocked over the monitor, but most likely we conclude that Jessica did not do it.

E. Peterson: For the part in blue the first thing it says is "TRUE STATEMENTS:"; therefore, all choices are true.

E. Peterson: Now for the red part, it could have been either Sandy, Nicole, or Jessica. It could have been Jessica because, out of fear of being in trouble, to get out of trouble she logically decided to lie and say it wasn't her. If it was Sandy she did immediately blame nicole, and in response Melissa said it was sandy, and Nicole almost cooly said that sandy was a liar; therefore, all was directed at Sandy. If it was Nicole, Sandy was telling the truth, and Melissa was probably trying to help Nicole from getting in trouble. Melissa probably did that because of their close relationship. It could not have been Melissa because no one pointed fingers at her nor did she respond so quickly. It all depends on the way you wanna see it, and your biases. Curtis Willson-Patterson: In both of the passages above ones logic played a key role in breaking the mystery of which answer in the a,b,c,d choice selection is correct. One has to interpret these passages from a rational standpoint by which they can show and or explain their reasoning in what they believe is the logical choice in the selections above. Curtis Wilson-Patterson: I looked at both of the passages and the answers were self explainatory. The answers were self explainatory in that most anyone from looking at those passages should be able to put one and two together to logically figure out the answers. For example in one of the passages(in the blue print) one had to choose from four options. Three out of the four options were false and all of them gave absolute answers except for one which said the number of false statements here is three.