In cases of inductive reasoning, even though the premises are true and the argument is " valid ", it is possible for the conclusion to be false ( determined to be false with a counterexample or other means ).

He used combinatorial tools in proving several of Stefan Banach's conjectures on Banach spaces and in constructing a Banach space with almost no symmetry, serving as a counterexample to several other conjectures.

A skew partition is a partition of a graph's vertices into two subsets, one of which induces a disconnected subgraph and the other of which has a disconnected complement ; had conjectured that no minimal counterexample to the strong perfect graph conjecture could have a skew partition.

One of the easiest ways of doing this is to find a counterexample which exhibits one property but not the other.

That such expansion can be obtained without a raise in taxes is due to growth of the tax digest and sound fiscal planning on the part of the board of commissioners, headed by Chairman Charles O. Emmerich who is demonstrating that the public trust he was given was well placed, and other county officials.

If you use a fiscal year, a year ending on the last day of any month other than December, your return is due on or before the 15th day of the 4th month after the close of your tax year.

You must attach a statement to your return, if you take advantage of this automatic extension, showing that you were in Alaska or were outside the United States or Puerto Rico on April 15 or other due date.

If the check is not good and the April 15 or other due date deadline elapses, additions to the tax may be incurred.

Lincoln's foreign policy approach had been initially hands off, due to his inexperience ; he left most diplomacy appointments and other foreign policy matters to his Secretary of State, William Seward.

Currently, a part of Algerian writers tends to be defined in a literature of shocking expression, due to the terrorism that occurred during the 1990s, the other party is defined in a different style of literature who staged an individualistic conception of the human adventure.

While the improvements are attributed primarily to changes in the brain and not just the hip and / or ankle joints, it is still unknown whether the improvements are due to adaptations in the cerebellum or compensation by other areas of the brain.

In the 17th and 18th centuries, there was much migration to Achill from other parts of Ireland, particularly Ulster, due to the political and religious turmoil of the time.

An abscess () is a collection of pus ( dead neutrophils ) that has accumulated in a cavity formed by the tissue in which the pus resides due to an infectious process ( usually caused by bacteria or parasites ) or other foreign materials ( e. g., splinters, bullet wounds, or injecting needles ).

This is likely due to three scenes in the Chronicles: first, when Eric paralyzes Corwin with an attack across the Trump and refuses to desist because one or the other would be dominated ; second, when Corwin faces the demon Strygalldwir, it is able to wrestle mentally with him when their gazes meet ; and third, when Fiona is able to keep Brand immobile in the final battle at the Courts of Chaos.

To prevent this unphysical situation from happening, Dirac proposed that a " sea " of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle, no other electron could fall into them.

Care should be taken that other vessels will not swing down on the boat due to the limited swing range.

It can be distinguished from other ambers via IR spectroscopy due to a specific carbonyl absorption peak.

In the early 20th century it was recognized that other cases such as carbon were due to differences in crystal structure.

Machiavelli goes on to reason that Agathocles ' success, in contrast to other criminal tyrants, was due to his ability to mitigate his crimes by limiting them to those that " are applied at one blow and are necessary to one's security, and that are not persisted in afterwards unless they can be turned to the advantage of the subjects ".

Australian rules football, officially known as Australian football, also called football, footy or Aussie rules However, late in the century the code began to decline in New South Wales and Queensland largely due to competition with other more popular football codes, as well as interstate rivalries and the lack of strong local governing bodies.

Olav Hammer suggests that anthroposophy carries scientism " to lengths unparalleled in any other Esoteric position " due to its dependence upon claims of clairvoyant experience, its subsuming natural science under " spiritual science ", and its development of what Hammer calls " fringe " sciences such as anthroposophical medicine and biodynamic agriculture justified partly on the basis of the ethical and ecological values they promote, rather than purely on a scientific basis.

Accordingly, Ben Adret addressed to the congregation of Montpellier a letter, signed by fifteen other rabbis, proposing to issue a decree pronouncing the anathema against all those who should pursue the study of philosophy and science before due maturity in age and in rabbinical knowledge.

While suitable media and raw pigments are available for the individual production of acrylic paint, due to the fast drying time and other technical issues, hand mixing may not be practical.

These conclusions were, however, questioned by another review, which found that clozapine, amisulpride, and olanzapine and risperidone were more effective Clozapine has appeared to be more effective than other atypical antipsychotics, although it has previously been banned due to its potentially lethal side effects.

* Amblyopia, decrease in acuity of one or both eyes due to poor transmission to the brain, often due to other conditions such as strabismus.

" It concluded, among other things, that Head Start programs designed to boost African-American IQ scores had failed, and that this was likely never to be remedied, largely because, in Jensen's estimation, 80 % of the variance in IQ in the population studied was the result of genetic factors and the remainder was due to environmental influences.

On September 11, 2001, Nami boarded United 93 and assisted in the hijacking of the plane, which crashed into a field in rural Shanksville, Pennsylvania, after a passenger uprising, due to the passengers receiving information from their families of the 3 other hijacked planes that hit the World Trade Center and the Pentagon.

Mainly due to reunification-related expenditures, Berlin as a German state has accumulated more debt than any other city in Germany, with the most current estimate being € 60 ($ 84 ) bn in December 2007.

Wilson, shackled and snarling, was thrown with the other prisoners and was soon joined by Green, McKee and McKinley.

McKee and Ross also applied for and were granted two patents, one in 1984 for a basic adjustable binding system and the other in 1985 for a patent for their adjustable plate type foot strap system.

Songs written by Tench and recorded by other artists include " You Little Thief ", a top 5 UK and Australian hit for Feargal Sharkey in 1985, ( written about his affair with Maria McKee, in response to her song " A Good Heart ") and " Never Be You " ( co-written with Petty ), which became a # 1 US Country hit for Rosanne Cash, also in 1985.

There are a Hershey's Chocolate Factory ( The Hershey Company ), a McKee Foods factory, and many other smaller factories.

During the Harrison administration, their daughter Mary Harrison McKee, her two children ; Caroline's father, and other relatives lived at the White House.

McKee has not benefited financially to the extent he might have: " I signed a contract where I only got a one-off payment and no repeat fees, but I've done quite well from a number of other things and I'm still exhibiting paintings.

The Republican representatives — Ó Brádaigh, Billy McKee and one other — felt a responsibility to pursue the opportunity, but were also skeptical of British intentions.

The only other person in the first film to use the phrase " graboid " is Val McKee ( Kevin Bacon ).

They discover that other survivors are already hiding in the cellar of the house: Harry Cooper ( Tom Towles ), his wife Helen ( McKee Anderson ), their daughter Sarah who was bitten on the arm by a zombie and has fallen seriously ill ; teenage redneck Tom Bitner ( William Butler ) and his girlfriend Judy Rose Larson ( Katie Finneran ).

Lonette McKee went on to other TV and film appearances, including playing Denzel Washington's on screen mother in Malcolm X, and Dorian Harewood and Philip Michael Thomas did more TV and film appearances.

McKee ’ s other credits include writing and presenting the BBC series Filmworks, the Channel Four series Reel Secrets, the BAFTA Award-winning J ' accuse Citizen Kane television program which he wrote and presented, and the writing of Abraham, the four-hour mini-series on Turner Network Television ( TNT ) that starred Richard Harris, Barbara Hershey and Maximilian Schell.

Poster Products Inc., Chicago, Ill.: a changeable copy and display sign which consists of an extruded impact styrene background in choice of colors, onto which are mounted snap-in letters, figures, or words screened on acetate or other types of sheet stock.

Residential building consists of houses, apartments, hotels, dormitories and other buildings designed for shelter.

Pure altruism consists of sacrificing something for someone other than the self ( e. g. sacrificing time, energy or possessions ) with no expectation of any compensation or benefits, either direct, or indirect ( e. g., receiving recognition for the act of giving ).

The family consists of a single genus Xeronema with two species, one found only on the Poor Knights islands in New Zealand and the other in New Caledonia.

No neuron ever has more than one axon ; however in invertebrates such as insects or leeches the axon sometimes consists of several regions that function more or less independently of each other.

The Amber multiverse consists of Amber, a city at one pole of the universe wherein is found the Pattern, the symbol of Order ; The Courts of Chaos, an assembly of worlds at the other pole where can be found the Logrus, the manifestation of Chaos, and the Abyss, the source or end of all reality ; and Shadow, the collection of all possible universes ( shadows ) between and around them.

Primitive Baptists in the Appalachian region often used " New Britain " with other hymns, and sometimes sing the words of " Amazing Grace " to other folk songs, including titles such as " In the Pines ", " Pisgah ", " Primrose ", and " Evan ", as all are able to be sung in common meter, of which the majority of their repertoire consists.

It consists of two electrodes: one made of zinc, the other of copper.

In the West, astrology most often consists of a system of horoscopes that claim to explain aspects of a person's personality and predict future events in their life based on the positions of the sun, moon, and other planetary objects at the time of their birth.

The other SNC group consists of 10 former members of the IU's SNC who reunited 10 years after their college years.

The town largely consists of the Milnshaw, Peel, Central, Barnfield and Spring Hill wards, although some parts of those wards are in other towns in the borough.

The first group consists of politicians which argue that the internationalization of the economy is essential for the development of the country, while the other group rely on interventionism, and protection of state enterprises.

According to bundle theory, an object consists of its properties and nothing more: thus neither can there be an object without properties nor can one even conceive of such an object ; for example, bundle theory claims that thinking of an apple compels one also to think of its color, its shape, the fact that it is a kind of fruit, its cells, its taste, or at least one other of its properties.

A block cipher consists of two paired algorithms, one for encryption, E, and the other for decryption, D. Both algorithms accept two inputs: an input block of size n bits and a key of size k bits ; and both yield an n-bit output block.

Each hour consists of headlines on each quarter hour, extended at the top of the hour to form the main part of the daily schedule though these are interspaced with other programmes, generally at weekends.

The Americas collection mainly consists of 19th and 20th century items although the Inca, Aztec, Maya and other early cultures are well represented ; collecting of modern artefacts is ongoing.

As with other baleen whales, its diet consists almost exclusively of small crustaceans known as krill.

Storage consists of storage devices and their media not directly accessible by the CPU, ( secondary or tertiary storage ), typically hard disk drives, optical disc drives, and other devices slower than RAM but are non-volatile ( retaining contents when powered down ).

The event consists of a number of individual contra dances, divided by a scattering of other partner dances, perhaps one or more waltzes, schottisches, polkas, or Swedish hambos.

The other part of a nation's money supply consists of bank deposits ( sometimes called deposit money ), ownership of which can be transferred by means of cheques, debit cards, or other forms of money transfer.

The Faculty Board is the faculty's representative body and consists of 18 elected faculty representatives as well as other senior administration officials.

A carbohydrate is an organic compound that consists only of carbon, hydrogen, and oxygen, usually with a hydrogen: oxygen atom ratio of 2: 1 ( as in water ); in other words, with the empirical formula.

The diet of a hypercarnivore consists of more than 70 % meat, that of a mesocarnivore 50-70 %, and that of a hypocarnivore less than 30 %, with the balance consisting of non-animal foods, which may include fungi, fruits, and other plant material.