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I have a question which asks if $X \supseteq I$. Is it just the same as $I \subseteq X$?

Because I never saw it the other way around or learned about it, I'm confused.

user7530
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Seth Keno
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    yes it is. {}{} – mookid Mar 15 '14 at 02:00
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    It's the exact same. Sometimes this is done only to make a sentence flow better but it's completely avoidable if your sentence is framed properly. – Cameron L. Williams Mar 15 '14 at 02:04
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    Sometimes it appears in constructions like "let $x\in U\supseteq V$" – user7530 Mar 15 '14 at 02:08
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    There is perhaps one caveat to be aware of. Some mathematical logic texts (usually older ones) use the symbol $\supset$ as alternative symbol for logical implication. – David H Mar 15 '14 at 02:10
  • The usage as a notation for implication (see the comment by @DavidH) has also been mentioned in this question: http://math.stackexchange.com/questions/391217/using-p-supset-q-instead-of-p-implies-q – Martin Sleziak Mar 15 '14 at 10:35

2 Answers2

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Wikipedia article about subset says:

If $A$ and $B$ are sets and every element of $A$ is also an element of $B$, then:

  • $A$ is a subset of (or is included in) $B$, denoted by $A \subseteq B$,

or equivalently

  • $B$ is a superset of (or includes) $A$, denoted by $B \supseteq A$.
Martin Sleziak
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Taking from mookid, so we have an answer, yes.

Ross Millikan
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    Yes to "is there a difference between $\subseteq$ to $\supseteq$" or yes to "Is $X \supseteq I$ just the same as $I \subseteq X$"? :) –  Mar 15 '14 at 10:07