SOLUTION: Could you please help me with solving this? Without writing them down what are the number of subsets of the set A = {a, b, c, d, e, f}? Of set B = {a, b, c, d, e, f, g, h, i, j

Take any subset of A, say S. There are 5 elements in A.
Therefore there are five questions we can ask about the 
subset S, relative to each member of A:

1. Does S contain "a" as a member? (Yes or No)
2. Does S contain "b" as a member? (Yes or No)
3. Does S contain "c" as a member? (Yes or No)
4. Does S contain "d" as a member? (Yes or No)
5. Does S contain "e" as a member? (Yes or No)
6. Does S contain "f" as a member? (Yes or No)

There are 2 ways to answer question 1, so that's 2 ways.

For each of those 2 ways to answer question 1, 
there are 2 ways to answer question 2, so that's 2^2 ways.

For each of those 2^2 ways to answer questions 1 and 2, 
there are 2 ways to answer question 3, so that's 2^3 ways.
ways. 

For each of those 2^3 ways to answer questions 1 thru 3, 
there are 2 ways to answer question 4, so that's 2^4 ways.
ways. 

For each of those 2^4 ways to answer questions 1 thru 4, 
there are 2 ways to answer question 5, so that's 2^5 ways.
ways. 

For each of those 2^5 ways to answer questions 1 thru 5, 
there are 2 ways to answer question 6, so that's 2^6 ways.
ways.

So that makes 2^6 or 64 subsets, counting the empty or null
set as one subset and the entire set as another subset.

When we answer "no" to all 6 questions, that is the null set.
When we answer "yes" to all 6 questions, that is the entire set.

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So in general,

A set that contains n elements or members has exactly 2^n subsets.

Therefore

B = {a, b, c, d, e, f, g, h, i, j}

has 10 members or elements, so B has 2^10 or 1024 subsets.

Edwin