Let *A _{i}* = {…,−2,−1, 0, 1,…,

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Step 1Here, Ai = {…,−2,−1, 0, 1,…, i}={ xϵ Z| x≤i }Step 2a) If i≤ then Ai is the subset of An.Ai C An. Taking union both sides.{:[uuu_(i=1)^(n)A_(i)subeuuu_(i=1)^(n)A_(n)],[uuu_(i=1)^(n)A_(i)subeuuu_(i=1)^(n)A_(n)=A_(n)]:}(1) using idempotent lawStep 3by definition of union,A_(n)subeuuu_(i=1)^(n)A_(i)dots..(2)Step 4From (1) and (2), the sets shou ... See the full answer