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List all eight subsets of the set $$A=\{3,5,7\}$$.

Let $$A=\{j,m,h\}$$ Explain why $\{A\}$ is not a subset of $A$.

We notice that the given set $A$ is finite. It contains three elements: 3, 5 and 7.

cryptomath
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  • Did you mean to label both sets as $ A $ ? – Q the Platypus Apr 07 '16 at 05:27
  • @QthePlatypus Yes. Anything else that is unclear please do not hesitate to ask – cryptomath Apr 07 '16 at 05:31
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    What gave you the impression that A is not a subset of itself? The eight subsets of A include both A and the empty set. – Quinn Greicius Apr 07 '16 at 05:34
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    Unfortunately, all of this is unclear. What do you mean "first eight sets of $A$"? Are you asking for all eight subsets of $A$? And what does $A = {j, m, h}$ have to do with the definition of $A$, and how do you use it to come to the (wrong) conclusion that $A$ is not a subset of $A$? –  Apr 07 '16 at 05:34

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Every set includes itself as a subset. A is a subset of A so the subsets of A are

$ \mathbb{P}(A) = \{ \{\}, \{3\}, \{5\}, \{7\}, \{3, 5\}, \{3, 7\}, \{5, 7\}, \{3, 5, 7\} \} $

Q the Platypus
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  • What of the $A{j,m,h}$? Should we presume that the set $A$ is variable and can take on any integers? – cryptomath Apr 07 '16 at 05:47
  • Since $ A = {3,4,7} = {j, m, h} $ then j must be one of 3, 4 or 7. However it shouldn't matter to the question. What motivated you to add that part. if I knew where it came from I could give a better answer. – Q the Platypus Apr 07 '16 at 05:59
  • Much obliged. Thanks for the help. – cryptomath Apr 07 '16 at 06:00