Since {1, 2, . . . , 6} is the set of all possible outcomes...

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Since {1, 2, . . . , 6} is the set of all possible outcomes of athrow with a regular die, the set of all possible outcomes of athrow with two dice is Throws := {1, 2, . . . , 6} Ã— {1, 2, . . . ,6}. We define eleven subsets P2, P3, . . . , P12 of Throws asfollows: Pk := {: m + n = k} for k âˆˆ {2, 3, . . . ,12}. For example, P3 is the set of all outcomes for which the sumof the two numbers of dots thrown is 3.
(a) Show that the sets P2, P3, . . . , P12 form a partition ofthe set Throws.
(b) Let R be the equivalence relation on Throws that has P2, P3,. . . , P12 as its equivalence classes. Give a definition of R bymeans of a description.
(c) Give a complete system of representatives for theequivalence relation R.

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GivenLet S be the set of all possible outcomes of twodicesthereforeS 11 12 13 14 15 16 21 22 23 24 25 2631 32 33 34 35 3641 42 43 44 45 4651 52 53 54 55 5661 62 63 64 65 66According to QuestionPk m n kP2 11P3 12 21P4 13 31 22P5 14 41 23 See Answer

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