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 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 symmetric association scheme is commutative.

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 connected graph is an expander ; however, different connected graphs have different expansion parameters.

:"[...] Every invariant and co-variant thus becomes expressible by a graph precisely identical with a Kekuléan diagram or chemicograph.

* Every tree is a bipartite graph and a median graph.

Every tree with only countably many vertices is a planar graph.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

* Every connected graph with only countably many vertices admits a normal spanning tree.

In mathematics, Tait's conjecture states that " Every 3-connected planar cubic graph has a Hamiltonian cycle ( along the edges ) through all its vertices ".

Every homomorphism of the Petersen graph to itself that doesn't identify adjacent vertices is an automorphism.

Every directed acyclic graph has a topological ordering, an ordering of the vertices such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge.

* Every planar graph whose faces all have even length is bipartite.

Every vertex of this graph has an even degree, therefore this is an Eulerian graph.

Every Eulerian orientation of a connected graph is a strong orientation, an orientation that makes the resulting directed graph strongly connected.

Every maximal outerplanar graph satisfies a stronger condition than Hamiltonicity: it is node pancyclic, meaning that for every vertex v and every k in the range from three to the number of vertices in the graph, there is a length-k cycle containing v. A cycle of this length may be found by repeatedly removing a triangle that is connected to the rest of the graph by a single edge, such that the removed vertex is not v, until the outer face of the remaining graph has length k.

Every outerplanar graph is a planar graph.

Every outerplanar graph is also a subgraph of a series-parallel graph.

Every forest, and every cactus graph is outerplanar.

Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.

Every adult and wise woman without husband although reserves the right to accept concubinage for her employer / master without any coercion or force, but Islamic scholars have consensus that for sex relations options of Nikkah and Muta should be adopted instead of concubinage in this era.

Every quark in the universe does not attract every other quark in the above distance independent manner, since colour-confinement implies that the strong force acts without distance-diminishment only between pairs of single quarks, and that in collections of bound quarks ( i. e., hadrons ), the net colour-charge of the quarks cancels out, as seen from far away.

Every Duke thereafter has either died without heirs or succeeded to the Crown, and so has not been able to leave the Royal Family.

Every autumn, according to Plutarch ( Life of Lycurgus, 28, 3 – 7 ), the Spartan ephors would pro forma declare war on the helot population so that any Spartan citizen could kill a helot without fear of blood or guilt ( crypteia ).

Every Indian who receives a land allotment " and has adopted the habits of civilized life " ( lived separate and apart from the tribe ) is bestowed with United States citizenship " without in any manner impairing or otherwise affecting the right of any such Indian to tribal or other property "

Every Planet and Satellite seems suspended in space, without any support ; performing their annual and diurnal revolutions without any apparent cause ".

Every Shintaido practice begins with warming-up exercises designed to soften and extend the body until it can move naturally, without the tensions of everyday life.

Every type of terminal had a hard-wired communications card which supported only the operation of one type of terminal without compatibility with other types of terminals on the same line.

Every feast day is preceded ( or followed, as with Shrove Tuesday followed by Ash Wednesday ) by a fast as well, in part to avoid the excessive revelry of pagan feasting without moderation.

Every fourth Coptic year is a leap year without exception, as in the Julian calendar, so the above mentioned new year dates apply only between 1900 and 2099 inclusive in the Gregorian Calendar.

# Every document can be rapidly searched, stored and retrieved without user knowledge of where it is physically stored.

Every household in the United States is authorized to discharge up to 220 pounds of hazardous waste per month to the sewage treatment plant legally without reporting it.

Every person with or without a Social Security Number is eligible to apply, however if a person does not meet any of the above criteria or is a documented resident of the United States, his or her claim can only be taken on paper and will be immediately denied.

" Every one of the six concertos set a precedent in scoring, and every one was to remain without parallel.

Every Athenian freemen whom he captured was sent back to the Athenians without ransom to encourage them to join the rebellion.

Every Afghan shall have the right, according to provisions of law, to print and publish on subjects without prior submission to state authorities.

Every year tens of millions of people around the world, including around four million cancer patients and 0. 8 million HIV / AIDS patients at the end of their lives suffer from such pain without treatment.

Every Zone has three Acts, 2 involving standard levels, and the third Act being a boss fight against Robotnik, without any flicky-collecting involved.

* South Carolina, 1712-" Be it enacted by the authority aforesaid, That no master, mistress, overseer, or other person whatsoever, that hath the care and charge of any negro or slave, shall give their negroes and other slaves leave ... to go out of their plantations .... Every slave hereafter out of his master's plantation, without a ticket, or leave in writing, from his master ... shall be whipped ...."

* Every person will enjoy the possession of his property of every nature, and dispose of it with the most perfect liberty, without any one being able to impede him.

( 1 ) Every individual is equal before and under the law and has the right to the equal protection and equal benefit of the law without discrimination and, in particular, without discrimination based on race, national or ethnic origin, colour, religion, sex, age or mental or physical disability.