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A sideways U with a bar beneath, allowing the two sets to be identical.
Also known as: Is a subset of or equal to, Contained in or equal
The subset-or-equal sign allows the possibility that the two sets are the same. Which of the two subset signs means what is genuinely unsettled: many authors use the plain sideways U for any subset including equality, so the barred form is the only one whose meaning can be relied on without checking the book's conventions.
States that every element of the left set is in the right set, and permits the two to be equal.
Contexts: Mathematics
Is the unambiguous member of a genuinely ambiguous pair: the unbarred sign means 'subset, possibly equal' to some authors and 'proper subset' to others, so a text using both should be read for its stated convention.
Contexts: Mathematics
A sideways U opening rightwards with a short horizontal line ruled directly beneath it.