# Example: Partitions of SetsLet A 1, 2, 3, 4, 5, 6}, A,= {1,2}, A,= {3,4} and A= {5, 6}Is {A1, A2, A3} a partition of A?а.b.Let Z be the set of all integers and let:To {n E Zn = 3kT, {nE Zn = 3k + 1, for some integer k}, andT2 {n E Z n = 3k + 2, for some integer k }.Is {To, T,, T2 } a partition of Z?for some integer k}0

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discrete math help_outlineImage TranscriptioncloseExample: Partitions of Sets Let A 1, 2, 3, 4, 5, 6}, A,= {1,2}, A,= {3,4} and A= {5, 6} Is {A1, A2, A3} a partition of A? а. b. Let Z be the set of all integers and let: To {n E Zn = 3k T, {nE Zn = 3k + 1, for some integer k}, and T2 {n E Z n = 3k + 2, for some integer k }. Is {To, T,, T2 } a partition of Z? for some integer k} 0 fullscreen
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It is known that the collection of disjoints subset of a given set or if the union of the subs... help_outlineImage TranscriptioncloseHere A 1,2A{3,4},4, = {5,6} Find the union of the sets as follows 4UA, 1,2,3,4 and A, U.A(3,4,5,6} Find the union of all A as follows. AU.A2UA1,2,3,4,5,6} A2NA = and 4 I 4 Also A,nA Thus, the collection of sets {4,A,,A are the partition of A fullscreen

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