Here I have a problem that asks me to determine whether the first set is the subset of the second, or the second set is the subset of the first, or neither is a subset of the other.
1st set = the set of airline flights from New York to New Delhi 2nd set = the set of nonstop airline flights from New York to New Delhi
The solution offered by the book is as follows: Because every nonstop flight is a flight, every element in the first set is also an element in the second set, so the first set is a subset of the second. Because there are flights that do have intermediate stops (say, from New York to Atlanta with a stop in Detroit), the second set is not a subset of the first.
To me it seems that the first set would consist of all flights including nonstop flights and flights with intermediate stops, so that the second set would be a subset of the first.
I'm not sure if I'm overthinking it or just missing something that is very clear and obvious.
Thank you in advance for any help! Much appreciated!
The book made an error in labelling.
As every non-stop flight is a flight the set of non-stop flights is a subset of the set of flights.
And as not ever flight is non-stop the set of flights is not a subset of the set of non-stop flights.
Now the book seems have mixed things up and is claiming 1st set = set of non-stop flights and 2nd set = set of flights.
BUT clearly in the beginning it was claiming the exact opposite.
It was a mistake. It doesn't matter what we label the as long as we are consistent. Which the book wasn't.
Upshot
If $A = $set of non-stop flights and $B =$ set of flights then:
$A \subset B$ and $B \not \subset A$.
I think you understand and get this.