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If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

A complete multipartite graph is a graph that is a complete k-partite graph for some positive integer k (Chartrand and Zhang 2008, p. 41).

The formal term in propositional calculus for the connective implies.

A theorem in set theory stating that, for all sets A and B, the following equivalences hold, A subset B<=>A intersection B=A<=>A union B=B.

Informally, a situation in which a decision must be made from several alternatives, none of which is obviously the optimal one. In formal logic, a dilemma is a specific type ...

The term in logic used to describe the operation commonly known as OR. A literal is considered a (degenerate) disjunction (Mendelson 1997, p. 30). The Wolfram Language ...

A disjunctive syllogism is a valid argument form in propositional calculus, where p and q are propositions: (p v q; ¬p)/(∴q). For example, if someone is going to study law or ...

The matrix operations of 1. Interchanging two rows or columns, 2. Adding a multiple of one row or column to another, 3. Multiplying any row or column by a nonzero element.