Mathematics, 05.05.2020 16:46 robert7248

Let S = {A1, A2, A3, A4, A5} be a collection of five subsets of the set A = {−5, −4, . . . , 4, 5}, where A1 = {x ∈ A : 1 < x2 < 10} A2 = {x ∈ A : (x + 2)(x − 4) > 0} A3 = {x ∈ A : |x + 2| + |x − 3| ≤ 5} A4 = {x ∈ A : 1 x2+1 > 2 5 } A5 = {x ∈ A : sin πx 4 = 0}. A relation R is defined on S by Ai R Aj (1 ≤ i, j ≤ 5) if Ai and Aj are numerically equivalent. According to Theorem 11.1, R is an equivalence relation. Determine the distinct equivalence classes for this equivalence relation.

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Let S = {A1, A2, A3, A4, A5} be a collection of five subsets of the set A = {−5, −4, . . . , 4, 5},...