Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a propositional function can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.

It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("∀x", "∀(x)", or sometimes by "(x)" alone). Universal quantification is distinct from existential quantification ("there exists"), which asserts that the property or relation holds only for at least one member of the domain.

Quantification in general is covered in the article on quantification (logic). Symbols are encoded U+2200 ∀ FOR ALL (HTML ∀ · ∀ · as a mathematical symbol).

Enrique Peña Nieto

Enrique Peña Nieto (Spanish pronunciation: [enˈrike ˈpeɲa ˈnjeto]; born 20 July 1966) is the 57th President of Mexico. His six-year term began in 2012. A member of the Institutional Revolutionary Party (PRI), he served as governor of the State of Mexico from 2005 to 2011. Peña Nieto was declared "president-elect" after the 2012 general election was declared valid by the Federal Electoral Tribunal, amidst accusations of electoral fraud. He took office on 1 December 2012, succeeding Felipe Calderón.

Pena Nieto announced his presidential candidacy in September 2011, four days after leaving office as governor. He formally registered in November 2011. Peña Nieto garnered a plurality of 39% of the vote and does not hold a legislative majority. His election marked the return of the PRI to power after a twelve-year hiatus. The PRI had governed Mexico uninterrupted for 71 years until it was defeated by the National Action Party (PAN) in 2000. Protests against the election of Peña Nieto drew tens of thousands of people across Mexico, particularly from the Yo Soy 132 student movement, who protested alleged voting irregularities and media bias. Others protested that during its time in power, the PRI became a symbol of corruption, repression, economic mismanagement and electoral fraud. Many Mexicans and urban dwellers worried that its return to power might signify a return to Mexico's past. Peña Nieto promised that his government would be much more democratic, modern and open to criticism. He also pledged to continue the fight against organized crime and drug trade and that there would be no pacts with criminals.

Enrique Peña Sánchez

Enrique Peña Sánchez (Puerto Padre, Las Tunas Province, 17 July 1880 – Havana, 13 April 1922) was a leading Cuban cornet player, orchestra leader and composer.

Born in a small town in the old province of Oriente, Peña studied with Marcos González and José Santos Betancourt. In 1902 he moved to Havana, and founded the band La Juventud, with himself as director and cornet, Rogelio Solis (double bass), Félix González (figle), José Belén Puig (first clarinet), José Urfé (second clarinet), José de los Reyes (kettle drum) and Rufino Cárdenas (güiro). This band had several members who became well known; Puig went on to become a famous leader of his own charanga. The band functioned until 1906.

His second band was called the Orquesta típica de Enrique Peña. Its line-up was Peña (cornet); Antonio González (trombone); Féliz González (figle); José Belén Puig (1st clarinet); José Urfé (2nd clarinet); Julián Barreto (violin); Alfredo Sáenz (violin); José de los Reyes (tympani); Rufino Cárdenas (güíro) and unknown (double bass). This orchestra became famous for being the first to play El bombín de Barreto (Barreto's bowler hat), written by Urfé, which was supposedly the first danzón to incorporate a syncopated third part, influenced by the son. The group recorded about 150 numbers, some of which are available on CD.