5. The Descarte product of k sets A1, A2, . , A (where k 1 is...

 

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5. The Descarte product of k sets A1, A2, . , A (where k 1 is a fixed integer), is the set of all length k, ordered sequence (tuples) whose ith component belong : to A;; denoted A x A x... x Ak = {(a1, a2,...,ak) a A, i = 1, 2,..., k} When A =A = = AB, we write Bk for k identical versions of B. Describe the set B when B = {0,1}, how many elements does BR have? (each element is a binary vector/sequeceu of length )? Visualize Bk when k = 2, k = 3 and k = 4, known that: i) each element is plotted by a point, ii) two points u, v B are connected by an edge if and only if u, v differ precisely at one coordinate. (If we call the Hamming distance between u, v is d(u, v)=uvil i=1 then u, v are connected when d(u, v) = 1). - 5. The Descarte product of k sets A1, A2, . , A (where k 1 is a fixed integer), is the set of all length k, ordered sequence (tuples) whose ith component belong : to A;; denoted A x A x... x Ak = {(a1, a2,...,ak) a A, i = 1, 2,..., k} When A =A = = AB, we write Bk for k identical versions of B. Describe the set B when B = {0,1}, how many elements does BR have? (each element is a binary vector/sequeceu of length )? Visualize Bk when k = 2, k = 3 and k = 4, known that: i) each element is plotted by a point, ii) two points u, v B are connected by an edge if and only if u, v differ precisely at one coordinate. (If we call the Hamming distance between u, v is d(u, v)=uvil i=1 then u, v are connected when d(u, v) = 1). -