__Explanation__:

Let’s take an example of 4 element set

{ a, b, c, d}

Now we need to find “**tuples of the form (A,B) such that A and B are subsets of S**”.

- Let’s take
**A** as {a} , now calculate how many **B**’s are possible such that **A****⊆****B**.

8 tuples are possible.

Now if we take Φ as **A** then total 16 tuples are possible . and

If we take {a, b} as **A **then total 4 tuples are possible and for A we can chose ^{n}C_{2 } ways so total ^{n}C_{2 }× 4 tuples are possible for 2 element in A. And so on we can calculate for 2 element subsets and 3 element subsets.

So its general form for no of tuples possible (if n elements are given :

^{n}C_{0}×(2^{n}) + ^{n}C_{1}×(2^{n-1}) + ^{n}C_{2}×(2^{n-2}) + ...+ ^{n}C_{n}×(2^{0}) = (2+1)^{n}

__Calculation __:

We have given number of elements as 10 so total number of tuples will be (2+1)^{10} = 3^{10 }= 59049.