Clarify the difference between a set being an element of a set, and a set being a subset of another set.
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Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – user1176409 Jul 12 '23 at 15:22
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For $S={\color{blue}{1}, , \color{red}{{1}}}$, the set $\color{red}{{1}}$ is an element of the set $S$ and the set ${\color{blue}{1}}$ is a subset of the set $S$. – Anurag A Jul 12 '23 at 15:35
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This looks like an exam question. Therefore you need to provide the answer that you have been taught. In set theory the situation is clear: $a\in b$ is the primitive (postulated) relation (and it means "$a$ is element of $b$") whereas $a\subset b$ is defined as $(\forall x)(x\in a\implies x\in b)$. However, depending on how you have been taught set theory, this answer may be good, or too high level, or too terse etc. – Jul 12 '23 at 15:51
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1Does this answer your question? Set theory: difference between belong/contained and includes/subset? – Mauro ALLEGRANZA Jul 13 '23 at 14:53