Venn diagram in the context of "Probability"

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.

The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of naive set theory. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied.

In logic, mathematics and linguistics, and (${\displaystyle \wedge }$) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ${\displaystyle \wedge }$ or ${\displaystyle \&}$ or ${\displaystyle K}$ (prefix) or ${\displaystyle \times }$ or ${\displaystyle \cdot }$ in which ${\displaystyle \wedge }$ is the most modern and widely used.

The and of a set of operands is true if and only if all of its operands are true, i.e., ${\displaystyle A\land B}$ is true if and only if ${\displaystyle A}$ is true and ${\displaystyle B}$ is true.

Intersectionality is an analytical framework for understanding how groups' and individuals' social and political identities result in unique combinations of discrimination and privilege. Examples of these intersecting and overlapping factors include gender, caste, sex, race, ethnicity, class, sexuality, religion, disability, physical appearance, and age. These factors can lead to both empowerment and oppression.

Intersectionality arose in reaction to both white feminism and the then male-dominated Black liberation movement, citing the "interlocking oppressions" of racism, sexism and heteronormativity. It broadens the scope of the first and second waves of feminism, which largely focused on the experiences of women who were white, cisgender, and middle-class, to include the different experiences of women of color, poor women, immigrant women, and other groups, and aims to separate itself from white feminism by acknowledging women's differing experiences and identities.

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics.Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and suffices for the everyday use of set theory concepts in contemporary mathematics.

Sets are of great importance in mathematics; in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory suffices for many purposes, while also serving as a stepping stone towards more formal treatments.

In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as ${\displaystyle \lor }$ and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula ${\displaystyle S\lor W}$, assuming that ${\displaystyle S}$ abbreviates "it is sunny" and ${\displaystyle W}$ abbreviates "it is warm".

In classical logic, disjunction is given a truth functional semantics according to which a formula ${\displaystyle \phi \lor \psi }$ is true unless both ${\displaystyle \phi }$ and ${\displaystyle \psi }$ are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an inclusive interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well as the numerous mismatches between classical disjunction and its nearest equivalents in natural languages.

Educational entertainment, also referred to by the portmanteau edutainment, is media designed to educate through entertainment. The term has been used as early as 1933. Most often it includes content intended to teach but has incidental entertainment value. It has been used by academia, corporations, governments, and other entities in various countries to disseminate information in classrooms and/or via television, radio, and other media to influence viewers' opinions and behaviors.

An Euler diagram (/ˈɔɪlər/, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between different sets, the Euler diagram shows only relevant relationships.

The Swiss mathematician Leonhard Euler (1707–1783) is one of the most important authors in the history of this type of diagram, but he is only the namesake, not the inventor. Euler diagrams were first developed for logic, especially syllogistics, and only later transferred to set theory. In the United States, both Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement of the 1960s. Since then, they have also been adopted by other curriculum fields such as reading as well as organizations and businesses.

A homophone (/ˈhɒməfoʊn, ˈhoʊmə-/) is a word that is pronounced the same as another word but differs in meaning or in spelling. The two words may be spelled the same, for example rose (flower) and rose (past tense of "rise"), or spelled differently, as in rain, reign, and rein. The term homophone sometimes applies to units longer or shorter than words, for example a phrase, letter, or groups of letters which are pronounced the same as a counterpart. Any unit with this property is said to be homophonous (/həˈmɒfənəs/).

Homophones that are spelled the same are both homographs and homonyms. For example, the word read, in "He is well read" and in "Yesterday, I read that book".

A homograph (from the Greek: ὁμός, homós 'same' and γράφω, gráphō 'write') is a word that shares the same written form as another word but has a different meaning. However, some dictionaries insist that the words must also be pronounced differently, while the Oxford English Dictionary says that the words should also be of "different origin". In this vein, The Oxford Guide to Practical Lexicography lists various types of homographs, including those in which the words are discriminated by being in a different word class, such as hit, the verb to strike, and hit, the noun a strike.

If, when spoken, the meanings may be distinguished by different pronunciations, the words are also heteronyms. Words with the same writing and pronunciation (i.e. are both homographs and homophones) are considered homonyms. However, in a broader sense the term "homonym" may be applied to words with the same writing or pronunciation. Homograph disambiguation is critically important in speech synthesis, natural language processing and other fields. Identically written different senses of what is judged to be fundamentally the same word are called polysemes; for example, wood (substance) and wood (area covered with trees).

In arithmetic and number theory, the least common multiple (LCM), lowest common multiple, or smallest common multiple (SCM) of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0.

The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions.

In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the logical connective used to conjoin two statements ${\displaystyle P}$ and ${\displaystyle Q}$ to form the statement "${\displaystyle P}$ if and only if ${\displaystyle Q}$" (often abbreviated as "${\displaystyle P}$ iff ${\displaystyle Q}$"), where ${\displaystyle P}$ is known as the antecedent, and ${\displaystyle Q}$ the consequent.

Nowadays, notations to represent equivalence include ${\displaystyle \leftrightarrow ,\Leftrightarrow ,\equiv }$.

John Venn, FRS, FSA (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in logic, set theory, probability, statistics, and computer science. In 1866, Venn published The Logic of Chance, a groundbreaking book which espoused the frequency theory of probability, arguing that probability should be determined by how often something is forecast to occur as opposed to "educated" assumptions. Venn then further developed George Boole's theories in the 1881 work Symbolic Logic, where he highlighted what would become known as Venn diagrams.