How Many Students Like Either Reading or Jogging?

[tzx9633]

Homework Statement

In a school . 35 students like reading , 50 student like jogging , and 15 students like both . How many person like either reading or sports ?

The ans is 35+ 50 -15 = 70 ( Ans given)

but , i think the ans should be 20+ 35 = 55 only

Which is correct ? If my ans is wrong , in what circumstances , the ans would be 20+ 35 = 55 ??

Homework Equations

The Attempt at a Solution

 

[MarkFL]

I agree with your Venn diagram, and I guess it just boils down to how we interpret "like either reading or sports." It we take that to mean likes one or the other, but not both, then it is 55, but if we take it to mean likes at least one of the two, then it is 70.

 

[Mark44]

I agree with your Venn diagram, and I guess it just boils down to how we interpret "like either reading or sports." It we take that to mean likes one or the other, but not both, then it is 55, but if we take it to mean likes at least one of the two, then it is 70.

The "either reading or sports" should be interpreted as the exclusive or, not the inclusive or. IOW, the ones who like reading don't like sports, and the ones who like sports don't like reading. Without the word "either" it would be reasonable to assume that some like both activities.

 

[MarkFL]

The "either reading or sports" should be interpreted as the exclusive or, not the inclusive or. IOW, the ones who like reading don't like sports, and the ones who like sports don't like reading. Without the word "either" it would be reasonable to assume that some like both activities.

I agree, and that's how I would interpret it as well, just as the OP did.

 

[Ray Vickson]

Homework Statement

In a school . 35 students like reading , 50 student like jogging , and 15 students like both . How many person like either reading or sports ?

The ans is 35+ 50 -15 = 70 ( Ans given)

but , i think the ans should be 20+ 35 = 55 only

Which is correct ? If my ans is wrong , in what circumstances , the ans would be 20+ 35 = 55 ??

Homework Equations

The Attempt at a Solution

In Logic and in Probability the word "or" (almost always) means "inclusive or", so "A or B" normally means "A or B or both". In set language this would be $A \cup B$, while "A or B but not both" would be $(A-B) \cup (B-A) = A \cup B - A \cap B$.

However, to be honest, it becomes a bit trickier when the word "either" is inserted, as it is in your case; then I think the situation is less settled. I have seen it interpreted in different ways in different sources.

 

[tzx9633]

"A or B" normally means "A or B or both"

Thanks for the point !

 

[Mark44]

However, to be honest, it becomes a bit trickier when the word "either" is inserted, as it is in your case; then I think the situation is less settled. I have seen it interpreted in different ways in different sources.

I agree with what you said regarding "A or B," but most of the cases I've seen with "either A or B," the intended meaning is one of the two alternatives, but not both. I can't cite any authoritative mathematical sources for this, but the Merriam-Webster dictionary defines "either-or" as "an unavoidable choice or exclusive division between only two alternatives".

Side note: Thread moved to the Precalc section.

 

[Ray Vickson]

I agree with what you said regarding "A or B," but most of the cases I've seen with "either A or B," the intended meaning is one of the two alternatives, but not both. I can't cite any authoritative mathematical sources for this, but the Merriam-Webster dictionary defines "either-or" as "an unavoidable choice or exclusive division between only two alternatives".

Side note: Thread moved to the Precalc section.

Your citation of "an unavoidable choice or exclusive division between only two alternatives" should be very helpful to the OP, because he/she needs to ask: is every student forced to like either jogging or reading but never both? That would be an unavoidable choice between two alternatives. Furthermore, when WE count the cases we are not performing any choice at all, we are just sorting the data, so we probably are not performing an unavoidable choice either.

I looked further into this on-line, by Googling "either-or in probability"; just about every web page (some including the word "either" and some not) use the inclusive-or form.

So, for the OP: the bottom line is that your book agrees with most others on the subject. That is the reason for the computation it performed.

Perhaps a more extreme example may help. Suppose that in a particular group of 100 students, 90 take physics, 90 take chemistry and 85 take both. How many students take either physics or chemistry? One (purely arithmetical) answer is 90 + 90 = 180, but this goes against the "spirit" of the question. A more complete statement of the question might be "In this group of 100 students, how many take either physics or chemistry?" My previous version of the question just left out the part in red, but I think most people would agree that it is probably implicit.