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Find the union and intersection of these families, and prove your answers?
n is element of Natural number
An = {4n, 4n +1, ..., 5n} for each natural number n..
1 Answer
- az_lenderLv 75 years ago
The intersection of all such sets is empty. To see that, consider A1 = {4,5} and A3 = {12,13,14,15}, which do not intersect.
The union of all such sets ALMOST all natural numbers; it excludes 1,2,3,6,7,and 11, but all the rest of the natural numbers are in the union.
Reasoning: You've got A1 and A3 above, and A2 = {8,9,10}, A4 = {16,17,18,19,20}. Note that A4 and A5 overlap at 20. Higher values of "n" will always involve overlaps between An and A(n+1), as
5n will be greater than or equal to 4(n+1), provided n is at least 4.
