Is This Answer Correct...Please Check For Me

The President’s Council on Fitness asked adults who exercise if they walk, run or stretch. Of those adults surveyed, how many ran and walked?

Here is the Venn diagram of the results:
http://www.flickr.com/photos/62474130@N0…

My answer: 20

Also, could you help me with this:
Write down all possible subsets of set Q using correct set notation.

Can you help me a little bit please? Thank you!

Here is the diagram:
http://www.flickr.com/photos/62474130@N0…

1) since it did not ask , " how many ran and walked only" the answer is 35, because the overlap between walking and running includes 20 who only ran and walked, but 15 more who ran,walked, and stretched.
In other words if you were in the group of 15, you would say, yes I walk, and, yes I run.

2)Q={a,c,k,p}

Subsets can be empty, or full or anything in between.

(four elements -> 2^4 subsets)

no elements: {} or null set
One element: {a}, {c}, {k}, {p}
two elements: {a,c}, {a,k}, {a,p}, {c,k}, {c,p}, {k,p}
Three elements {a,c,k} , {a,c,p} , {a,k,p}, {c,k,p}
Four elements {a,c,k,p}

Hoping this helps!

Almost right. 20 is the number of adults who ran and walked but didn't stretch. When you include the numbder who walked, ran and stretched, it brings the number who ran and walked to 35.
As for your second problem, Q has 4 elements. The number of subsets a set can have will be 2 raised to the power of how many elements there are. [This is because for each element, you can choose whether or not it wil be in a certain subset, leading to 2 choices for each element, meaning the total number of ways to choose is 2^n, n being the number of elements] So, we can expect to list 16 elements. Other counting arguments lead to the fact that there will be 1 subset with four elements, 4 with three elements, 6 with two elements, 4 with one element and 1 with no elements. [The correspondence to a certain row of Pascal's triangle is not a coincidence.] Listing them all shouldn't prove too hard, except that the correct set notation will be to surround them with { } and place commas in between each element, EXCEPT for the subset with no elements, the null set, which is a circle with a line through it, with no brackets. Good luck!

sorry....you need to count even those which also stretched

Q = { a , c ,k , p }...4 one term sets ...6 two term sets , 4 three term sets , 1 four term set

{ 4 choose 1 , four choose 2 , 4 choose 3 , 4 choose 4 }