SOLUTION: How many subsets can be made from in U={a,b,c,d}

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Question 1084197: How many subsets can be made from in U={a,b,c,d}
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
There are n = 4 elements in the set. So there are 2^n = 2^4 = 16 different subsets possible.

Those 16 subsets are:
{a,b,c,d}
{a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}
{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}
{a}, {b}, {c}, {d}
{ }

Note: { } denotes the empty set

Each line shown above represents a grouping of sets. For example, all of the sets with 3 items in them, such as {a,b,d}, are all on the same line. This is a handy way to group things. If you wish to list it all out where each set gets its own line then you'd write it like this

{a,b,c,d}
{a,b,c}
{a,b,d}
{a,c,d}
{b,c,d}
{a,b}
{a,c}
{a,d}
{b,c}
{b,d}
{c,d}
{a}
{b}
{c}
{d}
{}

Further Reading:

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
See the lesson
    - How many subsets are there in a given finite set of n elements?
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Miscellaneous word problems".



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