Logical conjunction

conjunctionANDlogical AND
In logic, mathematics and linguistics, And is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true. The logical connective that represents this operator is typically written as

Union (set theory)

unionset unionunions
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.

Educational aims and objectives

learning outcomeslearning objectiveAims and objectives
In some organisations the term learning outcome is used in the part of a course description where aims are normally found. One can equate aims to intended learning outcomes and objectives to measured learning outcomes. A third category of learning outcome is the unintended learning outcome which would include beneficial outcomes that were neither planned nor sought but are simply observed. Bloom's taxonomy, a classification of learning objectives. Educational assessment. Educational psychology. Instructional scaffolding. Mastery learning. Model of hierarchical complexity. Rubric (academic).

Interquartile mean

The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores.


NOTlogical negationnegated
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, which is interpreted intuitively as being true when P is false, and false when P is true. Negation is thus a unary (single-argument) logical connective. It may be applied as an operation on notions, propositions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes truth to falsity and vice versa.


In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number (pure number).

Complement (set theory)

complementset differencecomplements
In set theory, the complement of a set

Universal quantification

universal quantifieruniversally quantifieduniversal
In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a propositional function can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.


basketball playerhigh school basketballmen's basketball
Popular descriptions of positions include: Point guard (often called the "1") : usually the fastest player on the team, organizes the team's offense by controlling the ball and making sure that it gets to the right player at the right time. Shooting guard (the "2") : creates a high volume of shots on offense, mainly long-ranged; and guards the opponent's best perimeter player on defense. Small forward (the "3") : often primarily responsible for scoring points via cuts to the basket and dribble penetration; on defense seeks rebounds and steals, but sometimes plays more actively.

Parallel random-access machine

PRAMparallel random access machineconcurrent random access machine
In computer science, a parallel random-access machine (PRAM) is a shared-memory abstract machine. As its name indicates, the PRAM was intended as the parallel-computing analogy to the random-access machine (RAM). In the same way that the RAM is used by sequential-algorithm designers to model algorithmic performance (such as time complexity), the PRAM is used by parallel-algorithm designers to model parallel algorithmic performance (such as time complexity, where the number of processors assumed is typically also stated).

Existential quantification

existential quantifierthere exists
This is because \emptyset denotes the empty set, and no x of any description – let alone an x fulfilling a given predicate P(x) – exist in the empty set. See also vacuous truth. In category theory and the theory of elementary topoi, the existential quantifier can be understood as the left adjoint of a functor between power sets, the inverse image functor of a function between sets; likewise, the universal quantifier is the right adjoint. Symbols are encoded and. First-order logic. List of logic symbols – for the unicode symbol ∃. Quantifier variance. Quantifiers. Uniqueness quantification.

Transitive relation

transitivetransitivitytransitive property
In mathematics, a binary relation


textbookstext bookschool textbooks
A textbook is a comprehensive compilation of content in a branch of study. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textbooks and other books used in schools. Today, many textbooks are published in both print format and digital formats.

Grading in education

grade point averageGPAgrades
Grading in education is the process of applying standardized measurements of varying levels of achievement in a course. Grades can be assigned as letters (for example A through F), as a range (for example 1 to 6), as a percentage of a total number of questions answered correctly, or as a number out of a possible total (for example out of 20 or 100).

Empty set

In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is [[0|zero]]. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.

Transitive closure

extendtransitive closure first-order logictransitively-closed
In mathematics, the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive.

Set (mathematics)

setsetsmathematical set
One way is by intensional definition, using a rule or semantic description: The second way is by extension – that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets: One often has the choice of specifying a set either intensionally or extensionally. In the examples above, for instance, A = C and B = D. In an extensional definition, a set member can be listed two or more times, for example,. However, per extensionality, two definitions of sets which differ only in that one of the definitions lists members multiple times define the same set. Hence, the set is identical to the set.

Domain of discourse

universe of discoursedomainarea of interest
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

Decidability (logic)

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined. A theory (set of sentences closed under logical consequence) in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory.

SL (complexity)

SLsymmetric logspaceundirected connectivity
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component. This problem is also called the undirected reachability problem. It does not matter whether many-one reducibility or Turing reducibility is used.

Deviation (statistics)

deviationabsolute deviationdeviations
In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation (positive or negative), reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference.

Teacher's Highland Cream

Teacher's Highland Cream is a brand of blended Scotch whisky produced in Glasgow, Scotland, by Beam Suntory, the US-headquartered subsidiary of Suntory Holdings of Osaka, Japan. The Teacher's Highland Cream brand was registered in 1884. (The label on the bottles says "est. 1830", reflecting an earlier date when the founding family entered the whisky business, before the brand name was created.) Teacher's states that it uses "fully smoked peat single malt whisky from The Ardmore distillery as its fingerprint whisky" along with about 30 other single malt whiskies. Most of the output of the Ardmore distillery is used to produce the Teacher's brand.

Guarded logic

guarded fragmentguarded
They successfully transferred key properties of description, modal, and temporal logic to predicate logic. It was found that the robust decidability of guarded logic could be generalized with a tree model property. The tree model can also be a strong indication that guarded logic extends modal framework which retains the basics of modal logics. Modal logics are generally characterized by invariances under bisimulation. It also so happens that invariance under bisimulation is the root of tree model property which helps towards defining automata theory. Within Guarded Logic there exists numerous guarded objects. The first being guarded fragment which are first-order logic of modal logic.

L (complexity)

Llogarithmic spacelogspace
In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space. Formally, the Turing machine has two tapes, one of which encodes the input and can only be read, whereas the other tape has logarithmic size but can be read as well as written. Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags, and many basic logspace algorithms use the memory in this way.