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The power set of $\\left\\{\\var{x},\\var{y}\\right\\}$ is

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$\\left\\{\\left\\{\\right\\}, \\left\\{\\var{x}\\right\\},\\left\\{\\var{y}\\right\\}, \\left\\{\\var{x},\\var{y}\\right\\}\\right\\}$.

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You can obtain the power set by finding all the subsets of all possible sizes. Since we have a set of size two then the subsets have length at most two. These are

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• the subset of length zero: $\\left\\{\\right\\}$
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• the subsets of length one: $\\left\\{\\var{x}\\right\\},\\left\\{\\var{y}\\right\\}$
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• the subset length two: $\\left\\{\\var{x},\\var{y}\\right\\}$.
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Note that the length zero subset is always the empty set, and the largest subset is the set itself.

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The power set of $A$, written $P(A)$, is the set of all subsets of $A$.

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First we look at all the subsets containing zero elements. This is the empty set $\\left\\{\\right\\}$ and it is an element of any power set. Enter the empty set below using the NUMBAS syntax, which is set().

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Next we look at all the subsets containing exactly one element, such as $\\simplify{{set(x)}}$. Enter this using the NUMBAS syntax set({x}).

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What is the other subset that that contains exactly one element?

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What is the subset that contains exactly two elements?

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The power set is the set containg all these answers as elements. Enter your answer using the NUMBAS syntaxset(a,b,c,d)

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What is the power set of $\\simplify{{set(x,y)}}$?

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