Suppose H is a collection of hash functions, where each hash function h, is mapping the universe U of keys to {0, 1, · · · , m − 1}. Also, suppose that for every fixed pair (x, y) of keys (where x 6= y), and for any uniformly selected hash function h, the pair (h(x), h(y)) is equally likely to be any of the m2 pairs of elements from {0, 1, · · · , m − 1} (The probability is taken only over the random choice of the hash function.) Prove that H is a universal hashing.

Avegetable garden and a surrounding path are shaped like a square that together are 11ft wide. the path is 2ft wide. find the total area of the vegetable garden and path

Which themes are portrayed in this excerpt from leo tolstoy’s the death of ivan ilyich? praskovya fedorovna came of a good family, was not bad looking, and had some little property. ivan ilyich might have aspired to a more brilliant match, but even this was good. he had his salary, and she, he hoped, would have an equal income. she was well connected, and was a sweet, pretty, and thoroughly correct young woman. to say that ivan ilyich married because he fell in love with praskovya fedorovna and found that she sympathized with his views of life would be as incorrect as to say that he married because his social circle approved of the match. he was swayed by both these considerations: the marriage gave him personal satisfaction, and at the same time it was considered the right thing by the most highly placed of his associates. so ivan ilyich got married. conforming to social conventions criticism of a middle class lifestyle the destructive impact of loneliness struggling to face reality the necessity of companionship

Could somebody me with this radical simplification?