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Question: given a set m and two subset ni and n2...

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Given a set M and two subset Ni and N2, we call the intersection of i and N2, and we call the union of Ni and N2. (In mathematics, the word or means as much as and/or, e.g., if an element m M belongs to both Ni and N2, then it also belongs to the union. The mathematical or is not the same as either-or, which is also called the exclusive or.) To indicate that an object m E M does not belong to a subset N C M we write mfN. The set is called the complement of N in M, or just the complement of N. More generally, if i and N2 are subset of a set M, then is called the complement of N2 in Ni (iii) Put M = {x E Z | x is divisible by 2} and N2-{x E Z | x is divisible by 3). Describe the set Ni n N2. Is Z-i U N2? Does the complement of Ni U N2 in Z have infinitely many elements? Given two sets Mi and M2 (which may be the same), one can form the set of all ordered pairs (x, y) where z є Мі and y є M. One has (z, y)-(z, y) if and only if x-z and y-y. This set is called the product set and denoted by Mi x M2. (For instance, if M M2, then (x, y) and (y, r) both belong to MX M, but (z, y)メ(y,x) unless x-y.) iv) Let M and M2 be sets with finitely many elements. Show that |Mi x M2l M M2, .e. the cardinality of the product set Mi x M2 is equal to the product of the cardinalities of Mı and

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