Are there more fathers or sons?
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Original Question
On one logic test, we had the task of determining when there were more: fathers or sons.
My thinking was this: Every father is a son (of his parents), while every son is not a father because there are men who do not have children. Therefore, in any case, there are more sons.
However, when we got the results, it turned out that my task was not marked as correct. I asked for explanations from the professor.
His explanation was this: There are more fathers because there are fathers who have only daughters, that is, they have no sons.
We seem to be talking about different gatherings (different fathers and sons), but other than that, there is one problem in his explanation: Imagine we have 3 fathers. One has four sons, the other two sons and two daughters, and the third has only one daughter. Although the condition set by the professor has been met, there are again more sons than fathers because it is possible for a father to have more than one son.
Note: In order to be able to think at all whether there are more fathers or sons, we must start from the assumption that there are in a finite number.
Comments on Question
At the end of the day from the framing of the question, it would be uncertain if there were more sons that did not become fathers or more fathers that only had daughters. Without having a more robust question and consequently having it turn into a question for Mathematics, it seems you need to rely on the information at hand. Your counter example didn't help your cause though, because you used made up biased statistics to support your reasoning. An answer of uncertain should perhaps be the correct answer, but your answer should be as equally valid as the more fathers one. With no statistics to back either, there is no strong reason for either or to be the most. There must be an answer though and I think the question should have been phrased better. If perhaps was being counted multiple times over, I would side with your professor. It is ambiguous. Just like my rushed answer to this in the morning was.
There are more fathers because there are fathers who have only daughters, that is, they have no sons.
But what if those daughters go on to have sons themselves...? Hmm.
I would have to ask up front: fathers generally die before sons, so does this mean there are fatherless sons? Or are we considering dead people in this?
Answers
2This question is gender identity obsolete.
It's an interesting question that prompts me to think in two ways about it ... and also that reminds me of a related question I used to pose to my senior high school Maths students ... way back in the last millennium.
Thought 1 : To avoid a series of "Ya, but ..." responses, we would need to define our sample. The question is really easy to answer definitively if we were talking, for example, about all of the males living on a particular city block. At the same time, considering all males in the country might make it harder to come up with an exact answer, but in theory still possible. Still, it strikes me that if the aim is to move beyond a logic problem to determining the exact number of each, we'd need a well defined population.
Thought 2 : It seems like a good question to help folks understand the notion of infinity. As Shockwave mentioned, assuming a finite number of males might be needed.
My Remembering : Considering the potential for an infinite number of males, the description reminds me of a way I introduced the notion of infinity to some Maths classes. I would describe a hotel called "Hotel Infinity". Of course, it had an infinite number of rooms. Business was good and one day the hotel operator found that all of his rooms were full -- he was very happy about his good financial fortune. But shortly, "Infinity Bus Lines" arrived in his parking lot with a bus carrying (you guessed it!) an infinite number of passengers -- each one looking for a room.
The hotel owner was terribly disheartened at the prospects of having to turn away an infinite number of paying customers. Then, his daughter who was studying Infinity in her high school Maths class came up with a solution. She had her father move every existing guest into a different room. She moved each guest into a room with a room number double that of their original room ... so the folks in room 1 went into room 2 leaving room 1 empty, those in room 7 move into room 14, leaving room 7 empty, and so on. That put all of the existing guests into even numbered rooms and left the infinite number of odd numbered rooms empty ... and available for the infinite number of new guests who had just arrived on the bus.
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What we CAN conclude though (from your professor's answer) is that HE knows SHIT...