Necessity and sufficiency

In logic, necessity and sufficiency are implicational relationships between statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true or simultaneously false. In ordinary English, 'necessary' and 'sufficient' indicate relations between conditions or states of affairs, not statements. Being a male sibling is a necessary and sufficient condition for being a brother. Fred's being a male sibling is necessary and sufficient for the truth of the statement that Fred is a brother.

Definitions

In the conditional statement, "if S then N", the expression represented by S is called the antecedent and the expression represented by N is called the consequent. This conditional statement may be written in many equivalent ways, for instance, "N if S", "S implies N", "S only if N", "N is implied by S", S ⇒ N or "N whenever S".

Bleach

Bleach refers to a number of chemicals which remove color, whiten or disinfect, often by oxidation.

The bleaching process has been known for millennia, but the chemicals currently used for bleaching resulted from the work of several 18th century scientists. Chlorine is the basis for the most used bleaches, for example, the solution of sodium hypochlorite, which is so ubiquitous that most simply call it "bleach", and calcium hypochlorite, the active compound in "bleaching powder". Oxidizing bleaching agents that do not contain chlorine most often are based on peroxides, such as hydrogen peroxide, sodium percarbonate and sodium perborate. While most bleaches are oxidizing agents, some are reducing agents such as sodium dithionite and sodium borohydride.

Bleaches are used as household chemicals to whiten clothes and remove stains and as disinfectants, primarily in the bathroom and kitchen. Many bleaches have strong bactericidal properties, and are used for disinfecting and sterilizing and thus are used in swimming pool sanitation to control bacteria, viruses and algae and in any institution where sterile conditions are needed. They are also used in many industrial processes, notably in the bleaching of wood pulp. Bleach is also used for removing mildew, killing weeds and increasing the longevity of flowers.

Bleach (season 14)

The fourteenth season of the Bleach anime series, which is known as the Arrancar: Downfall arc (破面・滅亡篇, Arankaru Metsubō Hen), is directed by Noriyuki Abe and produced by TV Tokyo, Dentsu, and Studio Pierrot. The story will continue the fight between Soul Society's Soul Reapers and Sōsuke Aizen's arrancar army as the former defends Karakura Town from the latter's invasion, while Ichigo and his group fight the arrancars in Hueco Mundo to rescue Orihime Inoue.

The season started airing on April 13, 2010 in Japan on TV Tokyo. Aniplex collected it in eleven DVD volumes between February 23 and December 14, 2011. The English adaptation of the Bleach anime is licensed by Viz Media, and this season started airing on August 11, 2012.

The episodes uses six pieces of theme music: two opening themes and four closing themes. The first opening theme, "chAngE" by Miwa is used for episodes 266 to 291, while the second opening theme, "Ranbu no Melody" (乱舞のメロディ, Ranbu no Merodi, "Melody of the Wild Dance") by Sid is used from episode 292 to 316. The first ending theme, "Stay Beautiful" by Diggy-Mo is used for episodes 266 to 278, the second ending theme, "echoes" by Universe is used from episode 279 to 291, the third ending theme, "Last Moment" by SPYAIR is used from episode 292 to 303, and the fourth ending theme "Song For..." by ROOKiEZ is PUNK'D is used from episode 304 to 316.

Bleach (season 8)

The eighth season of the Bleach anime series is named the Arrancar: The Fierce Fight arc (破面・激闘篇, Arankaru Gekitō Hen). The episodes are directed by Noriyuki Abe and produced by TV Tokyo, Dentsu, and Studio Pierrot. Based on Tite Kubo's Bleach manga series, the episodes' plot centers on Ichigo Kurosaki's and his friends' battle against the Espada, the strongest members of former Soul Reaper captain Sōsuke Aizen's army, to save Orihime Inoue.

The season began airing on December 12, 2007 in Japan on TV Tokyo and ended on April 16, 2008. The English adaptation of the Bleach anime is licensed by Viz Media, and this arc began airing on September 26, 2009 and ended November 21, 2009 on Adult Swim. Four DVD compilations, each containing four episodes of the season, were released by Aniplex between May 28, 2008 and August 27, 2008 in Japan. Viz Media released the season in two separate DVD boxes during 2011 on June 21 and September 6. The first box, however, also contains episodes from the previous season.