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I've been struggling with this discrete mathematics question. Any clarification would be awesome, thanks!

{2} ⊆ {{1},{2}}

azimut
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MathNoob
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    because ${2}$ is an element of the ${{1},{2}}$. The correct statement is the following: ${{2}}\subset{{1},{2}}$ – RFZ Apr 12 '22 at 15:42
  • Possibly useful, almost a duplicate: https://math.stackexchange.com/questions/2620616/what-is-the-difference-between-x-and-x-when-x-itself-is-a-set/2620621#2620621 – Ethan Bolker Apr 12 '22 at 15:48
  • $2$ is an element of the set on the left, the right set has only elements {$1$} and {$2$}, hence $2$ is no element of this set. – Peter Apr 12 '22 at 15:54
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    hi MathNoob. here's a good question to start with; what are the elements of ${{1},{2}}$? and what does it mean for ${2}$ to be a subset of a set $X$? – Atticus Stonestrom Apr 12 '22 at 15:55

2 Answers2

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By definition, $X \subseteq Y$ if every element of $X$ is also an element of $Y$.

In your case, $X = \{2\}$ and $Y = \{\{1\},\{2\}\}$. So $X$ has the single element $2$, which is not among the two elements $\{1\}$ and $\{2\}$ of $Y$. (Note that $2 \neq \{2\}$.)

azimut
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  • This question seems not to meet the standards for the site. Instead of answering it, it would be better to look for a good duplicate target, or help the user by posting comments suggesting improvements. Please also read the meta announcement regarding quality standards. – Shaun Apr 12 '22 at 16:10
  • @Shaun Yeah, I was in the mood of just answering, it's a new contributor after all and he states that he has been struggling with this problem (which I can very well understand and which to me, is a good enough motivation to post this question). Let me remark that, while I'm not convinced that giving this answer is "bad" concerning MSE standards and etiquette, I'm pretty sure that the downvotes are clearly failing in this regard. – azimut Apr 12 '22 at 16:26
  • We all do it, @azimut. In fact, you might have seen that I posted a bit of a hint in the comments (before I deleted it). Just don't make a habit of it :) – Shaun Apr 12 '22 at 16:28
  • Shaun, now you showed him! Seriously, what are you trying to achieve? There is an "almost duplicate" in the comments, which is only an "almost duplicate" if you know the answer to this question. – gnasher729 Apr 12 '22 at 19:10
  • See the meta announcement, @gnasher729, linked to in the comment above. – Shaun Apr 12 '22 at 19:33
  • @Shaun: Frankly, I don't see how the meta announcement should apply in this situation. – azimut Apr 12 '22 at 20:48
  • You're free to disagree, @azimut. – Shaun Apr 12 '22 at 20:50
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Note that $\{\{1\},\{2\}\}$ is a set consists of two elements $\{1\},\{2\}$. The statements $\{2\} \subset \{\{1\},\{2\}\}$ is equivalent to that $2$ is an elements of $\{\{1\},\{2\}\}$, and this is not true (none of $\{1\},\{2\}$ is $2$).

  • This question seems not to meet the standards for the site. Instead of answering it, it would be better to look for a good duplicate target, or help the user by posting comments suggesting improvements. Please also read the meta announcement regarding quality standards. – Shaun Apr 12 '22 at 16:11