conditional propositions

Propositional Logic: 

Propositional Logic

Ambiguous Laws: 

Ambiguous Laws An old ordinance in Naperville IL stated “It shall be unlawful for any person to keep more than three dogs and three cats upon his property within the city.” If I live there and own five dogs, do I violate the ordinance? ANS: No; Having 5 dogs does not violate the ordinance that prohibits more than 3 dogs AND more than 3 cats.

From an IQ test: 

From an IQ test If all Zips are Zoodles, and all Zoodles are Zonkers, then all Zips are definitely Zonkers. The above sentence is logically: True or False. ANS: True.

From an IQ test: 

From an IQ test If some Wicks are Slicks, and some Slicks are Snicks, then some Wicks are definitely Snicks. The statement is: True or False. ANS False.

Programming errors: 

Programming errors A computer program instructs me to enter a number that is not equal to 0 or not equal to 1. If I do so, the program will continue; otherwise it aborts. What happens if I enter 2? How about 1? Either way one of the conditions is met and the program continues.

Analysis of Sherlock Holmes’ reasoning in a passage from “A Study In Scarlet.” : 

Analysis of Sherlock Holmes’ reasoning in a passage from “A Study In Scarlet.” And now we come to the great question as to the reason why. Robbery has not been the object of the murder, for nothing was taken. Was it politics, then, or was it a woman? That is the question which confronted me. I was inclined from the first to the latter supposition. Political assassins are only too glad to do their work and fly. The murder had, on the contrary, been done most deliberately, and the perpetrator has left his tracks all over the room, showing he had been there all the time. Conclusion: It was a woman.

Correlation: 

Correlation A measure of association between two variables. It measures how strongly the variables are related, or change, with each other. If two variables tend to move up or down together, they are said to be positively correlated.

Correlating Data: 

Correlating Data On weekends when there is a Packer game, there are more people in town. There is a strong correlation between Packer weekends and increased activity in town. Conclusion: packer games bring people to town. Is this a valid argument? No. The conclusion is true but the argument that draws this conclusion from the given data is false.

Correlating Data: 

Correlating Data Among people who smoke there is a higher incidence of lung cancer. There is a strong correlation between people who smoke and people who have lung cancer. Conclusion: smoking contributes to lung cancer. Is this a valid argument? No: The conclusion is true but the argument that draws this conclusion from the given data is false.

Correlating Data: 

Correlating Data The rate of violent incidents is much higher among people who watch violent shows. There is a strong correlation between people who watch violent shows and people who commit violent acts. Thus, watching violent shows contributes to increased violent acts. Is this a valid argument? No.

Correlating Data vs. Cause and Effect: 

Correlating Data vs. Cause and Effect Two sets of data that are positively correlated do not necessarily imply cause and effect between them. If it did, consider the following.

Correlating Data: 

Correlating Data If you examine the records of the city of Copenhagen for the ten or twelve years following World War II, you will find a strong positive correlation between (i) the annual number of storks nesting in the city, and (ii) the annual number of human babies born in the city. Conclusion: Storks bring babies. Again: an invalid argument; As population increased, there were more people to have babies, and therefore more babies were born. Also as population increased, there was more building construction to accommodate it, which in turn provided more nesting places for storks; hence increasing numbers of storks.

Correlating Data vs. Cause and Effect: 

Correlating Data vs. Cause and Effect It is possible that children behave violently for other reasons and are especially fond of watching violent television. The correlation between the two events is just not enough information to conclude anything about cause and effect. Thus, violent behavior is correlated to viewing violent television, but not necessarily caused by it.

Correlating Data vs. Cause and Effect: 

Correlating Data vs. Cause and Effect Two sets of data that are positively correlated may be the result of cause and effect; they may also be the result of a third condition.

Correlating Data: 

Correlating Data A certain group of people eat a lot of a certain type of food. That group also has a high incidence of heart disease. There is a strong correlation between the food and heart disease. Conclusion: Eating that food contributes to heart disease. Invalid argument: Perhaps people eat that food because of their culture. Also, perhaps their ethnicity has a genetic predisposition to obesity and heart disease. Thus, there’s no established cause and effect, just a correlation.

Formulating arguments: 

Formulating arguments Logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You visit the island and are approached by two natives who speak to you as follows: A says: B is a knight. B says: A and I are of opposite type. Who are A and B? Conclusion: A and B are both knaves.

Problem Solving: 

Problem Solving In the back of an old cupboard you discover a note signed by a pirate famous for his bizarre sense of humor and love of logical puzzles. In the note he wrote that he had hidden treasure somewhere on the property. He listed five true statements below and challenged the reader to use them to figure out the location of the treasure. If the house is next to a lake, then the treasure is not in the kitchen. If the tree in the front yard is an elm, then the treasure is in the kitchen. This house is next to a lake. The tree in the front yard is an elm or the treasure is buried under the flagpole. If the tree in the back yard is an oak, then the treasure is in the garage. Where is the treasure?

Problem Solving: 

Problem Solving (From the movie “The Labyrinth” starring Jim Bowie: There are two doors. One door leads in the right direction, the other one leads in the wrong direction. There are two people standing in front of the doors. One always lies, and one always tells the truth. You don't know which one is the liar, and you don't know which door is the wrong door. What one question can you ask that will tell you which door you should take? Point to a door and ask one: “Would the other person tell me this is the right door?”

Database applications: 

Database applications A database contains information on suppliers, parts, and what suppliers supply what part. Consider the statement: “There is no supplier for whom there is not a part that the supplier does not supply.” What does this mean?

Database applications(cont.): 

Database applications(cont.) All suppliers supply all parts No suppliers supply all parts Some supplier supplies all parts Some suppliers supply no parts No supplier supplies any parts All suppliers supply no parts All suppliers supply some parts ANS: b.

Reasoning and Logic: 

Reasoning and Logic From [http://www.holycross.edu/departments/socant/rsinglet/asranswers.htm#ch3] Reasoning is a thought process whereby one draws conclusions from information (i.e., evidence).  Logic analyzes the correctness of acts of reasoning by examining the relation between evidence and conclusion, enabling one to say whether the evidence logically justifies the conclusion.

Producing Invalid Conclusions Through Valid Arguments: 

Producing Invalid Conclusions Through Valid Arguments Either God can prevent suffering or He cannot. If He cannot, then He is not all powerful If He can prevent suffering and there is suffering, then He is not all good. There is suffering. Conclusion: Either God is not all powerful or He is not all good. This is a valid argument even though the conclusion may be false. This can happen if one of the premises is false.

A Valid Argument is not Necessarily a Sound Argument.: 

A Valid Argument is not Necessarily a Sound Argument. A Valid Argument follows logically from the premises. A Sound Argument follows logically from the premises AND the premises are True. A sound argument always has a true conclusion. A valid argument may have a false conclusion.

Some Other Examples:: 

Some Other Examples: [http://en.wikipedia.org/wiki/Logical_fallacy#Example_1]