Question: Quotient groups and subgroups together form a way of describing every group by its presentation: any group is the quotient of the free group over the generators of the group, quotiented by the subgroup of relations. The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses. Together with the relations
Is there an answer to this question: What is a finite composition of two symmetries or their inverses?

Answer: every symmetry of the square


Question: In 1839 Mariano Spada (1796 - 1872), professor of theology at the Roman College of Saint Thomas, published Esame Critico sulla dottrina dell’ Angelico Dottore S. Tommaso di Aquino circa il Peccato originale, relativamente alla Beatissima Vergine Maria [A critical examination of the doctrine of St. Thomas Aquinas, the Angelic Doctor, regarding original sin with respect to the Most Blessed Virgin Mary], in which Aquinas is interpreted not as treating the question of the Immaculate Conception later formulated in the papal bull Ineffabilis Deus but rather the sanctification of the fetus within Mary's womb. Spada furnished an interpretation whereby Pius IX was relieved of the problem of seeming to foster a doctrine not in agreement with the Aquinas' teaching. Pope Pius IX would later appoint Spada Master of the Sacred Palace in 1867.
Is there an answer to this question: What work asserted a problem between a doctrine of Pius IX and the teachings of Aquinas?

Answer: unanswerable


Question: The country was historically about evenly balanced between Catholic and Protestant, with a complex patchwork of majorities over most of the country. Geneva converted to Protestantism in 1536, just before John Calvin arrived there. One canton, Appenzell, was officially divided into Catholic and Protestant sections in 1597. The larger cities and their cantons (Bern, Geneva, Lausanne, Zürich and Basel) used to be predominantly Protestant. Central Switzerland, the Valais, the Ticino, Appenzell Innerrhodes, the Jura, and Fribourg are traditionally Catholic. The Swiss Constitution of 1848, under the recent impression of the clashes of Catholic vs. Protestant cantons that culminated in the Sonderbundskrieg, consciously defines a consociational state, allowing the peaceful co-existence of Catholics and Protestants. A 1980 initiative calling for the complete separation of church and state was rejected by 78.9% of the voters. Some traditionally Protestant cantons and cities nowadays have a slight Catholic majority, not because they were growing in members, quite the contrary, but only because since about 1970 a steadily growing minority became not affiliated with any church or other religious body (21.4% in Switzerland, 2012) especially in traditionally Protestant regions, such as Basel-City (42%), canton of Neuchâtel (38%), canton of Geneva (35%), canton of Vaud (26%), or Zürich city (city: >25%; canton: 23%).
Is there an answer to this question: How is a consociational state defined by the Constitution of 1848?

Answer: allowing the peaceful co-existence of Catholics and Protestants


Question: In the first year, 400 beer houses opened and within eight years there were 46,000 across the country, far outnumbering the combined total of long-established taverns, pubs, inns and hotels. Because it was so easy to obtain permission and the profits could be huge compared to the low cost of gaining permission, the number of beer houses was continuing to rise and in some towns nearly every other house in a street could be a beer house. Finally in 1869 the growth had to be checked by magisterial control and new licensing laws were introduced. Only then was it made harder to get a licence, and the licensing laws which operate today were formulated.
Is there an answer to this question: How many beer houses existed throughout Britain eight years after the passage of the Beer Act?

Answer:
46,000