Problem: Please answer a question about the following article about Group (mathematics):
In many situations it is desirable to consider two group elements the same if they differ by an element of a given subgroup. For example, in D4 above, once a reflection is performed, the square never gets back to the r2 configuration by just applying the rotation operations (and no further reflections), i.e. the rotation operations are irrelevant to the question whether a reflection has been performed. Cosets are used to formalize this insight: a subgroup H defines left and right cosets, which can be thought of as translations of H by arbitrary group elements g. In symbolic terms, the left and right cosets of H containing g are
When is it preferable to consider two group elements to be the same?
A: irrelevant to the question whether a reflection has been performed
Problem: Please answer a question about the following article about Southampton:
Archaeological finds suggest that the area has been inhabited since the stone age. Following the Roman invasion of Britain in AD 43 and the conquering of the local Britons in 70 AD the fortress settlement of Clausentum was established. It was an important trading port and defensive outpost of Winchester, at the site of modern Bitterne Manor. Clausentum was defended by a wall and two ditches and is thought to have contained a bath house. Clausentum was not abandoned until around 410.
What year did the Romans invade Britain?
A: AD 43
Problem: Please answer a question about the following article about Gamal Abdel Nasser:
Following the announcement of Nasser's death, Egypt and the Arab world were in a state of shock. Nasser's funeral procession through Cairo on 1 October was attended by at least five million mourners. The 10-kilometer (6.2 mi) procession to his burial site began at the old RCC headquarters with a flyover by MiG-21 jets. His flag-draped coffin was attached to a gun carriage pulled by six horses and led by a column of cavalrymen. All Arab heads of state attended, with the exception of Saudi King Faisal. King Hussein and Arafat cried openly, and Muammar Gaddafi of Libya fainted from emotional distress twice. A few major non-Arab dignitaries were present, including Soviet Premier Alexei Kosygin and French Prime Minister Jacques Chaban-Delmas.
How many people attended Nasser's funeral?
A: at least five million
Problem: Please answer a question about the following article about Police:
Edwin Chadwick's 1829 article, "Preventive police" in the London Review, argued that prevention ought to be the primary concern of a police body, which was not the case in practice. The reason, argued Chadwick, was that "A preventive police would act more immediately by placing difficulties in obtaining the objects of temptation." In contrast to a deterrent of punishment, a preventive police force would deter criminality by making crime cost-ineffective - "crime doesn't pay". In the second draft of his 1829 Police Act, the "object" of the new Metropolitan Police, was changed by Robert Peel to the "principal object," which was the "prevention of crime." Later historians would attribute the perception of England's "appearance of orderliness and love of public order" to the preventive principle entrenched in Peel's police system.
What did Chadwick say police should be focused on?
A:
prevention