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Recognizing partitions - sets of strings. (b) Let A be the set of words in the...

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Advance Math

Recognizing partitions - sets of strings.

(b) Let A be the set of words in the Oxford English Dictionary(OED). For each positive integer j, define Aj to be the set of allwords with j letters in the OED. For example, the word "discrete"is an element of A8 because the word "discrete" has 8 letters. Thelongest word in the OED is"pneumonoultramicroscopicsilicovolcanoconiosis" which has 45letters. You can assume that for any integer i in the range 1through 45, there is at least one word in the OED that has iletters. Do the sets A1, …, A45 form a partition of the set ofwords in the OED?

(don't give explanation with reflexive, symmetric andtransitive because we haven't learn it yet)

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