Set theory question

  • #1
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Homework Statement


Assume that ##x## and ##y## are members of a set ##B##. Show that ##\{ \{x\}, \{x,y\} \} \in \mathcal{P} \mathcal{P} B##

Homework Equations




The Attempt at a Solution


I know that ##\{ \{x\}, \{x,y\} \} \in \mathcal{P} \mathcal{P} B## iff ##\{ \{x\}, \{x,y\} \} \subseteq \mathcal{P} B##, but I don't see where this gets me. To me it's obviously true, but I don't see how to show it.
 

Answers and Replies

  • #2
FactChecker
Science Advisor
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If something seems obvious, just see if you can use the basic definitions to state it. State the definition of power set and start there.
Since x and y ∈ B, {x} and {x,y} are subsets of B. By the definition of the power set ......
 
  • #3
1,462
44
If something seems obvious, just see if you can use the basic definitions to state it. State the definition of power set and start there.
Since x and y ∈ B, {x} and {x,y} are subsets of B. By the definition of the power set ......
Oh, right. That seems really obvious now. So the power set of B is the set of all subsets. Since ##\{x\}## and ##\{x,y\}## are subsets of B, the set ##\{ \{x\}, \{x,y\} \}## must be a subset of the power set.
 

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