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To understand groups beyond the level of mere symbolic manipulations as above, more structural concepts have to be employed.c[›] There is a conceptual principle underlying all of the following notions: to take advantage of the structure offered by groups (which sets, being "structureless", do not have), constructions related to groups have to be compatible with the group operation. This compatibility manifests itself in the following notions in various ways. For example, groups can be related to each other via functions called group homomorphisms. By the mentioned principle, they are required to respect the group structures in a precise sense. The structure of groups can also be understood by breaking them into pieces called subgroups and quotient groups. The principle of "preserving structures"—a recurring topic in mathematics throughout—is an instance of working in a category, in this case the category of groups.
What has to be compatible with the group operation?
A: constructions related to groups

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In 1839, Melbourne resigned after Radicals and Tories (both of whom Victoria detested) voted against a bill to suspend the constitution of Jamaica. The bill removed political power from plantation owners who were resisting measures associated with the abolition of slavery. The Queen commissioned a Tory, Sir Robert Peel, to form a new ministry. At the time, it was customary for the prime minister to appoint members of the Royal Household, who were usually his political allies and their spouses. Many of the Queen's ladies of the bedchamber were wives of Whigs, and Peel expected to replace them with wives of Tories. In what became known as the bedchamber crisis, Victoria, advised by Melbourne, objected to their removal. Peel refused to govern under the restrictions imposed by the Queen, and consequently resigned his commission, allowing Melbourne to return to office.
Which party was Sir Robert Peel a part of?
A: Tory

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Just eight months into his presidency, the terrorist attacks of September 11, 2001 suddenly transformed Bush into a wartime president. Bush's approval ratings surged to near 90%. Within a month, the forces of a coalition led by the United States entered Afghanistan, which had been sheltering Osama bin Laden, suspected mastermind of the September 11 attacks. By December, the Taliban had been removed as rulers of Kabul, although a long and ongoing reconstruction would follow, severely hampered by ongoing turmoil and violence within the country.
By which month, were the Taliban no longer controlling Kabul?
A: December

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The CJK ideographs currently have codes only for their precomposed form. Still, most of those ideographs comprise simpler elements (often called radicals in English), so in principle, Unicode could have decomposed them, as it did with Hangul. This would have greatly reduced the number of required code points, while allowing the display of virtually every conceivable ideograph (which might do away with some of the problems caused by Han unification). A similar idea is used by some input methods, such as Cangjie and Wubi. However, attempts to do this for character encoding have stumbled over the fact that ideographs do not decompose as simply or as regularly as Hangul does.
What ideographs do not have codes for their precomposed form yet?
A:
unanswerable