In predicate logic, universal quantification formalizes the notion that something (a logical predicate) is true for everything, or every relevant thing. The resulting statement is a universally quantified statement, and we have universally quantified over the predicate. In symbolic logic, the universal quantifier (typically Failed to parse (Missing texvc executable; please see math/README to configure.): \forall , U+2200 ∀ , a turned A) is the symbol used to denote universal quantification, and is often informally read as "given any" or "for all". Universal quantification is distinct from existential quantification ("there exists"), which asserts that the property or relation holds for at least one member of the domain.

Quantification in general is covered in the article on quantification. Symbols are encoded U+2200 ∀ for all (HTML: ∀ ∀ as a mathematical symbol).

Suppose it is given that

2·0 = 0 + 0, and 2·1 = 1 + 1, and 2·2 = 2 + 2, etc.

This would seem to be a logical conjunction because of the repeated use of "and." However, the "etc." cannot be interpreted as a conjunction in formal logic. Instead, the statement must be rephrased:

John Roger Stephens (born December 28, 1978), better known by his stage name John Legend, is an American singer-songwriter and actor. He has won nine Grammy Awards, and in 2007, he received the special Starlight award from the Songwriters Hall of Fame.

Prior to the release of his debut album, Stephens' career gained momentum through a series of successful collaborations with multiple established artists. Stephens added his voice to those of other artists, assisting in them reaching chart-topper hits. He lent his voice to Kanye West's All of the Lights, on Slum Village's "Selfish" and Dilated Peoples' "This Way". Other artists included Jay-Z's "Encore", and he sang backing vocals on Alicia Keys' 2003 song "You Don't Know My Name" and Fort Minor's "High Road." Stephens played piano on Lauryn Hill's "Everything Is Everything."

Stephens was born on December 28, 1978, in Springfield, Ohio. He is the son of Phyllis, a seamstress, and John Mills, a factory worker and former National Guardsman. Throughout his childhood, Stephens was homeschooled on and off by his mother. At the age of four, he began playing the piano and at the age of seven, he performed with his church choir. When he was ten, his parents divorced, causing his mother to suffer a breakdown. At the age of 12, Stephens attended North High School, from which he graduated four years later. He graduated salutatorian.

Selena Marie Gomez (born July 22, 1992) is an American actress and singer best known for portraying Alex Russo in the Emmy Award-winning Disney Channel television series Wizards of Waverly Place. She subsequently ventured into feature films and has starred in the television movies Another Cinderella Story, Wizards of Waverly Place: The Movie, and Princess Protection Program. She made her starring theatrical film debut in Ramona and Beezus.

Her career has expanded into the music industry; Gomez is the lead singer and founder of the pop band Selena Gomez & the Scene, which has released three RIAA Gold certified studio albums, Kiss & Tell, A Year Without Rain, and When the Sun Goes Down, spawned three RIAA Platinum certified singles, "Naturally", "Who Says" and "Love You Like a Love Song" and charted four No. 1 Billboard Hot Dance Club Songs. Gomez has also contributed to the soundtracks of Tinker Bell, Another Cinderella Story, Wizards of Waverly Place, and Shake It Up after signing a record deal with Hollywood Records.

Kanye Omari West ( /ˈkɑːnjeɪ/; born June 8, 1977) is an American musician, film director and fashion designer. West first rose to fame as a producer for Roc-A-Fella Records, where he eventually achieved recognition for his work on Jay-Z's album The Blueprint, as well as hit singles for musical artists including Alicia Keys, Ludacris, and Janet Jackson. His style of production originally used pitched-up vocal samples from soul songs incorporated with his own drums and instruments. However, subsequent productions saw him broadening his musical palette and expressing influences encompassing '70s R&B, baroque pop, trip hop, arena rock, folk, alternative, electronica, synthpop, and classical music.

West released his debut album The College Dropout in 2004, his second album Late Registration in 2005, his third album Graduation in 2007, his fourth album 808s & Heartbreak in 2008, and his fifth album My Beautiful Dark Twisted Fantasy in 2010. West released a collaborative album, Watch the Throne with Jay-Z in 2011, which is the duo's first collaborative album. His five solo albums, all of which have gone platinum, have received numerous awards and critical acclaim. As of 2012, West has won a total of eighteen Grammy Awards, making him one of the most awarded artists of all-time. All albums have been very commercially successful, with My Beautiful Dark Twisted Fantasy becoming his fourth consecutive No. 1 album in the U.S. upon release. West has had 5 songs exceed 3 million in digital sales as of July 2011, with "Gold Digger" selling 3,086,000, "Stronger" selling 4,402,000, "Heartless" selling 3,742,000, "E.T." selling over 4,000,000 and "Love Lockdown" selling over 3,000,000 placing him third in overall digital sales of the past decade. He has sold over 30 million digital songs in the United States making him one of the best-selling digital artists of all-time.

Scott Ramon Seguro Mescudi (born January 30, 1984), better known by his stage name Kid Cudi ( /ˈkɪd ˈkʌdi/ KID KUD-ee), sometimes stylized KiD CuDi, is an American alternative hip hop recording artist, singer-songwriter, guitarist and actor. He first gained major attention after the release of his debut mixtape A Kid Named Cudi. In 2009, his single "Day 'n' Nite" reached the top five of the Billboard Hot 100 and Hot R&B/Hip-Hop Songs charts. "Day 'n' Nite" was included on Cudi's debut album Man on the Moon: The End of Day, which was later certified Gold. In 2010 he released his second studio album Man on the Moon II: The Legend of Mr. Rager, preceded by the release of two singles "Erase Me" and "Mr. Rager". In October 2010, Cudi announced that he would be forming a rock band with Dot da Genius called 'Wizard', later renamed WZRD. Their self-titled debut album was released on February 28, 2012. Kid Cudi has sold over 4.6 million digital singles and has worked with Kanye West, Common, David Guetta and other artists signed to the GOOD Music label.