Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

Every diagonal matrix is symmetric, since all off-diagonal entries are zero.

Every symmetric matrix is thus, up to choice of an orthonormal basis, a diagonal matrix.

Every real symmetric matrix is Hermitian, and therefore all its eigenvalues are real.

Every maximally symmetric space has constant curvature.

Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular.

Every symmetric group has a one-dimensional representation called the trivial representation, where every element acts as the one by one identity matrix.

Every symmetric operator is closable.

Every self-adjoint operator is maximal symmetric.

Every self-adjoint operator is densely defined, closed and symmetric.

Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree.

Every convex centrally symmetric polyhedron P in R < sup > 3 </ sup > admits a pair of opposite ( antipodal ) points and a path of length L joining them and lying on the boundary ∂ P of P, satisfying

Every state maintains its own bar association, supervised by that state's highest court.

Every year the association coordinates the day of French language within International Organisations ( 2010 ). It also organizes seminaries to increase awareness about the importance of linguistic, cultural and conceptual diversity.

After Go West, Young Man West starred in Every Day's a Holiday ( 1937 ) for Paramount before their association came to an end.

Every association of men is necessarily a separation from other men ... the political thus understood is not the constitutive principle of the state, of order, but a condition of the state.

Every year the association hosts Diamond, Golden and Silver jubilee functions, where alumni graduating 60, 50 and 25 years earlier are invited.

Every state in the United States has a regulatory body ( usually called a state bar association ) that polices lawyer conduct.

Every time we see a Nokia Mobile, the association between the two words ' Nokia ' and ' Phone ' gets strengthened in our mind.

Every association of men is necessarily a separation from other men ... the political thus understood is not the constitutive principle of the state, of order, but a condition of the state.

Every member of the association must ascribe to the NRB Statement of Faith and adhere to the rigorous NRB Code of Ethics.

Every year the association publishes a report about the state of the comics industry in France.

Every time they mention Kenny Garrett, there will probably be some association with Miles Davis, but at the same time, when they mention Herbie Hancock, they always mention Miles Davis, or Wayne Shorter.

Every Spring, each member of the association votes for two players.

Every student has to be affiliated with his or her department association and the General Students Association.

Every state besides Alaska and Georgia have their own state athletic training association that acts similar to the district associations as they have their own board members.

Every URL consists of some of the following: the scheme name ( commonly called protocol ), followed by a colon, two slashes, then, depending on scheme, a server name ( exp.

" I might easily have written this story in the traditional manner [...] Every novelist knows the recipe [...] It is not very difficult to follow a simple, chronological scheme which the critics will understand [...] But I, after all, am trying to tell the story of this Chapelizod family in a new way.

Every closed point of Hilb ( X ) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point.

Every backup scheme should include dry runs that validate the reliability of the data being backed up.

" Every expedient known to legal ingenuity has been resorted to by defendants and their confederates to avoid and defeat trials on the indictments found, but it is hoped and expected that at the next term of the court the trial and merited conviction of guilty parties to this stupendous scheme of fraud, perjury, and public robbery which has been developed, will be secured.

Every state and mission secondary school in Zambia has been provided with at least 10 computers through the scheme.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.