Difference between revisions of "The relationship between logical implication and the subset relation"
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| + | <math>A\subset B</math> (and we say "A is a subset of B") if and only if every element of <math>A</math> also belongs to <math>B</math> | ||
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| + | That is: <math>[A\subset B]\iff[x\in A\implies x\in B]</math><ref>Definition 3.10 (p10) - Introduction to Set Theory, Third Edition (Revised and Expanded) - Karel Hrbacek and Thomas Jech</ref> | ||
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| + | ==Sources== | ||
{{Definition|Set Theory}} | {{Definition|Set Theory}} | ||
Revision as of 18:46, 13 February 2015
Definition
[math]A\subset B[/math] (and we say "A is a subset of B") if and only if every element of [math]A[/math] also belongs to [math]B[/math]
That is: [math][A\subset B]\iff[x\in A\implies x\in B][/math][1]
Sources
- ↑ Definition 3.10 (p10) - Introduction to Set Theory, Third Edition (Revised and Expanded) - Karel Hrbacek and Thomas Jech
