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Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
In 2012, the head of AP Grading, Trevor Packer, stated that the reason for the low percentages of 5s is that "AP World History is a college-level course, & many sophomores aren't yet writing at that level." 10.44 percent of all seniors who took the exam in 2012 received a 5, while just 6.62 percent of sophomores received a 5.
Universe set and complement notation The notation L ∁ = def X ∖ L . {\displaystyle L^{\complement }~{\stackrel {\scriptscriptstyle {\text{def}}}{=}}~X\setminus L.} may be used if L {\displaystyle L} is a subset of some set X {\displaystyle X} that is understood (say from context, or because it is clearly stated what the superset X ...
It also arises in the description of the set difference in algebraic geometry (see below). (I : J) is sometimes referred to as a colon ideal because of the notation. In the context of fractional ideals, there is a related notion of the inverse of a fractional ideal.
The colon, :, is a punctuation mark consisting of two equally sized dots aligned vertically. A colon often precedes an explanation, a list, [1] or a quoted sentence. [2] It is also used between hours and minutes in time, [1] between certain elements in medical journal citations, [3] between chapter and verse in Bible citations, [4] and, in the US, for salutations in business letters and other ...
Advanced Placement (AP) examinations are exams offered in United States by the College Board and are taken each May by students. The tests are the culmination of year-long Advanced Placement (AP) courses, which are typically offered at the high school level. AP exams (with few exceptions [1]) have a multiple-choice section and a free-response ...
In Americanist phonetic notation, a colon may be used to indicate vowel length. This convention is somewhat less common than the half-colon. The IPA length mark. In the International Phonetic Alphabet, a special triangular colon-like letter is used to indicate that the preceding consonant or vowel is long. Its form is that of two triangles ...
Set-builder notation makes use of predicates to define sets. In autoepistemic logic , which rejects the law of excluded middle, predicates may be true, false, or simply unknown . In particular, a given collection of facts may be insufficient to determine the truth or falsehood of a predicate.