Similar ideas had been proposed before Venn. Christian Weise in 1712 ("Nucleus Logicoe Wiesianoe") and Leonhard Euler ("Letters to a German Princess") in 1768, for instance, came up with similar ideas. The idea was popularised by Venn in "Symbolic Logic", Chapter V "Diagrammatic Representation", 1881.
The following example uses two sets, A and B, represented here as coloured circles. The orange circle, set A, represents all living creatures that are two-legged. The blue circle, set B, represents the living creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that can both fly "and" have two legs—for example, parrots—are then in both sets, and hence correspond to points in the area where the blue and orange circles overlap. That area contains all such (and only) such living creatures.
Humans and penguins are bipedal, and hence are in the orange circle, but since they cannot fly, they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, and fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly (for example, whales and spiders) would all be represented by points outside both circles.
The combined area of sets A and B is called the "union" of A and B, denoted by . The union in this case contains all living creatures that are either two-legged, or that can fly (or both).
The area in both A and B, where the two sets overlap, is called the "intersection" of A and B, denoted by . For example, the intersection of the two sets is not empty, because there "are" points that represent creatures that are in "both" the orange and blue circles.
In the illustrations below the left circle shows set formula_1 and the right circle shows set formula_2. Results of operations are shown as colored areas.
Starbuck Island
Starbuck Island (or Volunteer Island) is a coral atoll in the central Pacific. It is part of the Central Line Islands of Kiribati. No one lives on the island.
Starbuck Island is located at . It is east-to-west and north-to-south. The island has a land area of . It is a low, dry, coral limestone island. It has a steep beach.
There is no freshwater on the island. Each year, the island gets about of rain.
Starbuck Island has a large colony of Sooty Terns. It is estimated that 1.5 million pairs of the birds live on the island. The island is also a home to Polynesian Rats, feral cats, Green turtles and about fifteen other species of seabirds.
Enrique Peña Nieto
Enrique Peña Nieto (born 20 July 1966) is a Mexican politician. He was the 57th President of Mexico from 2012 to 2018. He became President in 2012. Peña Nieto is a member of the Institutional Revolutionary Party (PRI). He was Governor of the State of Mexico from 2005 to 2011. Peña Nieto became President-elect after the 2012 general election was found to be valid by the Federal Electoral Tribunal, after some accusations of electoral fraud. He took office on 1 December 2012.
Nieto was born on 20 July 1966 in Atlacomulco, State of Mexico, a city 55 miles (89 km) northwest of Mexico City. He is the oldest of four siblings; his father, Gilberto Enrique Peña del Mazo, was an electrical engineer; his mother, María del Perpetuo Socorro Ofelia Nieto Sánchez, a schoolteacher. He is the nephew of two former governors of the State of México: on his mother's side, Arturo Montiel; on his father's, Alfredo del Mazo González. He attended Denis Hall School in Alfred, Maine, during one year of junior high school in 1979 to learn English. After living in Atlacomulco for the first 11 years of his life, Peña Nieto's family moved to the city of Toluca.
In 1975, his father would often take him to the campaign rallies of the State of Mexico's governor, Jorge Jiménez Cantú, a close friend of Peña del Mazo. The successor of the governor was Alfredo del Mazo González, a cousin of Peña Nieto's father. During Del Mazo González's campaign in 1981, the fifteen-year-old Peña Nieto had his first direct contact with Mexican politics: he began delivering campaign literature in favor of his relative, a memory Peña Nieto recalls as the turning point and start of his deep interest in politics.
In 1984 at the age of 18, Peña Nieto traveled to Mexico City and enrolled in the Panamerican University, where he earned a Bachelor of Arts (BA) degree in legal studies. Peña Nieto's academic thesis was found to contain some improper citations and plagiarism, which stirred controversy in May 2016. Peña Nieto sought a master's degree in Business Administration (MBA) at the Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM), based in the State of Mexico.
Peña Nieto joined the Institutional Revolutionary Party (PRI) in 1984, and with a law degree nearly completed, he began earning his own money. During his final years in college, Peña Nieto worked for a public notary in Mexico City, around the same time when his relative, Alfredo del Mazo González, was mentioned as a firm candidate for the 1988 presidential elections. In his twenties, he worked at the San Luis Industrial Corporation, an auto parts manufacturer, and at the law firm Laffan, Muse and Kaye. While still a student at the Universidad Panamericana, he roomed with Eustaquio de Nicolás, the current president of Homex, a leading Mexican construction and real estate company. He also befriended and roomed with Luis Miranda, who occupied several offices during the 1999–2000 administration in the State of Mexico.
Peña Nieto formally started his political career under the mentorship of Montiel Rojas, becoming the Secretary of the Citizen Movement of Zone I of the State Directive Committee of the National Confederation of Popular Organizations (CNOP), one of the three sectors of the PRI. For three consecutive years, Peña Nieto participated as a delegate to the Organization and Citizen Front in different municipalities of the State of Mexico. Then, between 1993 and 1998, during Emilio Chuayfett's term as governor, Peña Nieto was chief of staff and personal secretary to Montiel Rojas, the Secretary of Economic Development of the State of Mexico.
After 1999, Peña Nieto went from having low-level secretary positions to higher and more qualified offices. He served from 1999 to 2000 as the Sub-secretary of Government, and as financial sub-coordinator of the political campaign of Montiel Rojas. In 2001, Montiel Rojas named Peña Nieto Sub-secretary of Interior in the State of Mexico, a position that granted him the opportunity to meet and forge relationships with top PRI politicians and wealthy businessmen. After his term concluded, he served as the administrative secretary, as president of the Directive Council of Social Security, as president of the Internal Council of Health, and as vice president of the National System for Integral Family Development – all in the State of Mexico. Under the wing of Montiel Rojas, Peña Nieto formed a group known as the "Golden Boys of Atlacomulco" with other members of the PRI.
Peña Nieto was elected to a local deputy position in his hometown of Atlacomulco, State of Mexico, in 2003. Two years later, the governorship of the State of Mexico was sought by Atlacomulco-natives Carlos Hank Rhon, Isidro Pastor, Héctor Luna de la Vega, Guillermo González Martínez, Óscar Gustavo Cárdenas Monroy, Eduardo Bernal Martínez, Cuauhtémoc García Ortega and Fernando Alberto García Cuevas. Peña Nieto was among the crowd, but was not poised as one of the favorites. Nonetheless, in 2005, Peña Nieto was the last man standing, succeeding Montiel Rojas as governor of the State of Mexico. On 12 February 2005, with 15,000 supporters in attendance, he was sworn in as candidate for the PRI.