Question: Are Columbia University and Cornell University both private institutions?

full_context: Document 1: Harvard University: Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities.
Document 2: Princeton University: Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark in 1747, then to the current site nine years later, where it was renamed Princeton University in 1896.
Document 3: List of Columbia University alumni: This is a sorted list of notable persons who are alumni of Columbia University, New York City. For further listing of notable Columbians see: Notable alumni at Columbia College of Columbia University; Columbia University School of General Studies; Barnard College; Columbia Law School; Columbia Business School; Columbia University Graduate School of Journalism; Columbia Graduate School of Architecture, Planning and Preservation; Columbia University College of Physicians and Surgeons; Columbia University Graduate School of Education (Teachers College); Fu Foundation School of Engineering and Applied Science; Columbia Graduate School of Arts and Sciences; Columbia University School of Professional Studies; Columbia University School of the Arts; and the School of International and Public Affairs.
Document 4: List of presidents of Cornell University: The President of Cornell University is the chief administrator of Cornell University, an Ivy League institution located in Ithaca, New York and New York City. Included in the list below are all Presidents of Cornell University, from the first President Andrew Dickson White and through the current President, Martha E. Pollack. There have been 14 Presidents of Cornell University, not including three interregnum presidencies during university presidential transitions.
Document 5: Cornell Law School: Cornell Law School is the law school of Cornell University, a private Ivy League university located in Ithaca, New York. It is one of the five Ivy League law schools and offers three law degree programs (J.D., LL.M., and J.S.D.) along with several dual-degree programs in conjunction with other professional schools at the university. Established in 1887 as Cornell's Department of Law, the law school is ranked 13th in the United States by U.S. News & World Report.
Document 6: Cornell University: Cornell University ( ) is a private and statutory Ivy League research university located in Ithaca, New York. Founded in 1865 by Ezra Cornell and Andrew Dickson White, the university was intended to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's motto, a popular 1865 Ezra Cornell quotation: "I would found an institution where any person can find instruction in any study."
Document 7: Ithaca College: Ithaca College is a private, nonsectarian, coeducational liberal arts college located on the South Hill of Ithaca, New York, United States. The college was founded by William Egbert in 1892 as a conservatory of music and is set against the backdrop of the city of Ithaca, Cayuga Lake, waterfalls, and gorges. The college is best known for its large list of alumni who have played substantial roles in the media and entertainment industries.
Document 8: Pennsylvania State University: The Pennsylvania State University (commonly referred to as Penn State or PSU) is a state-related, land-grant, doctoral university with campuses and facilities throughout Pennsylvania. Founded in 1855, the university has a stated threefold mission of teaching, research, and public service. Its instructional mission includes undergraduate, graduate, professional and continuing education offered through resident instruction and online delivery. Its University Park campus, the flagship campus, lies within the Borough of State College and College Township. It has two law schools, Penn State Law, on the school's University Park campus, and Dickinson Law, located in Carlisle, 90 miles south of State College. The College of Medicine is located in Hershey. Penn State has another 19 commonwealth campuses and 5 special-mission campuses located across the state. Penn State has been labeled one of the "Public Ivies," a publicly funded university considered as providing a quality of education comparable to those of the Ivy League.
Document 9: Dartmouth College: Dartmouth College ( ) is a private Ivy League research university in Hanover, New Hampshire, United States. Established in 1769 by Eleazar Wheelock, it is the ninth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. Although founded as a school to educate Native Americans in Christian theology and the English way of life, Dartmouth primarily trained Congregationalist ministers throughout its early history before it gradually secularized, emerging at the turn of the 20th century from relative obscurity into national prominence.
Document 10: Yale University: Yale University is an American private Ivy League research university in New Haven, Connecticut. Founded in 1701, it is the third-oldest institution of higher education in the United States and one of the nine Colonial Colleges chartered before the American Revolution.
Document 11: Cornell University School of Hotel Administration: The School of Hotel Administration (SHA, more commonly known as the Hotel School) at Cornell University is a specialized business school in the SC Johnson College of Business at Cornell University, a private Ivy League university located in Ithaca, New York. Founded in 1922, it was the world's first four-year intercollegiate school devoted to hospitality management.
Document 12: List of Cornell University alumni: This list of Cornell University alumni includes notable graduates, non-graduate former students, and current students of Cornell University, an Ivy League university located in Ithaca, New York. Cornell counted 245,027 living alumni as of August 2008. Its alumni constitute 25 recipients of National Medal of Science and National Medal of Technology and Innovation combined, 32 MacArthur Fellows, 34 Marshall Scholars and 31 Rhodes Scholars, and Cornell is the only university with three female winners of unshared Nobel Prizes among its graduates (Pearl S. Buck, Barbara McClintock, and Toni Morrison). Many alumni maintain university ties through Homecoming's reunion weekend, through "Cornell Magazine", and through the Cornell Club of New York. In 2005, Cornell ranked #3 nationwide for gifts and bequests from alumni. Alumni are known as "Cornellians".
Document 13: Ivy League: The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism.
Document 14: New-York Central College, McGrawville: New-York Central College, McGrawville was an institution of higher learning founded by Cyrus Pitt Grosvenor and other anti-slavery Baptists in 1849 in McGraw, New York. The college was notable because it educated blacks as well as whites in the time of southern slavery and northern segregation, and educated women with men at a time when few institutions of higher learning were co-educational. In addition to the African-Americans in the student body, at least two of the school's faculty were black as well. Some of the school's funding came from New York State
Document 15: Columbia University: Columbia University (Columbia; officially Columbia University in the City of New York), established in 1754, is a private Ivy League research university in Upper Manhattan, New York City, often cited as one of the world's most prestigious universities.
ground_truth: yes