SOLUTION: What is the subset of T= {f,o,u,r}

You must not have understood what the word "subset" means.  The question you
should have asked is not

but this:

There are 16 subsets of T = {f,o,u,r}, not just one, as the way you worded the
question seems to show that you thought.  Here are the 16 subsetS:

 1. { }    <-- There is the empty subset, where you don't take any of the 
               members of the set T, which is {f,o,u,r}

Then there are the subsets where you take just 1 of the elements of {f,o,u,r}:
 2. {f}
 3. {o}
 4. {u}
 5. {r}

Then there are the subsets where you take just 2 of the elements of {f,o,u,r}: 
 6. {f,o}
 7. {f,u}
 8. {f,r}
 9. {o,u}
10. {o,r}
11. {u,r} 

Then there are the subsets where you take just 3 of the elements of {f,o,u,r}: 
12. {f,o,u}
13. {f,o,r}
14. {f,u,r}
15. {o,u,r}

Then there is just one "subset", called the "improper" subset, where we take
all four of the elements of {f,o,u,r}.  We call all the others "proper"
subsets, because they are properly "sub" (by the definition of "sub", which
means "not all of").  We like to consider a set to be "a subset of itself",
even though that's really not "proper".  So the set itself is the only
"improper" subset. So the "improper" subset is the set T itself:

16. {f,o,u,r}

The reason we like to call the empty set { } and the whole set "subsets", is
because doing so makes the formula for the number of subsets work, which is:

"The number of subsets of a set with N elements is 2N."

As you see from above the set {f,o,u,r} has 4 elements and the number of
subsets is 24 = (2)(2)(2)(2) = 16. 

And you see, as I said in the beginning, the question you should ask is not

but this:

Edwin