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 Question from Kats, a student: How Many sub sets are in set k={6,7,3}

Hi Kats,

Suppose you want to list all the possible subsets. Start with the element 6. You can start a subset by including 6 or not including 6. Thus there are $2$ subsets started,

1. $\{6$ and

2. $\{$

I haven't put in a closing $\}$ since I haven't completed building the subsets yet.

Now look at the element 7. I can continue each of the subsets I have started by including or not including 7. Thus at this point I have started $2 \times 2 = 4$ subsets,

1. $\{6, 7$

2. $\{6$

3. $\{7$ and

4. $\{$

Finally the last element 3. Again you can build on each of the $4$ subsets you have started by including 3 or not including 3. Now you can put in the closing $\}$ as the building is complete. How many are there? Can you list them all?

Write back if you ned more assistance,
Penny

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