If A = {62n - 35n - 1: n = 1, 2, 3, ...} and B = {35(n - 1) : n = 1,2,3,...} then which of the following is true?
Explanation:
For n = 1, A1 = 0
For n = 2, A2 = 1225 = 35 × 35
Also, 62n- 35n - 1 = (36n - 1) - 35n.
The term in the bracket 36n - 1 is always divisible by (36 - 1) or by 35. Similarly 35n is also always divisible by 35. Therefore each term in the set A is divisible by 35. However, not all positive multiples of 35 are present in set A.
For n = 1, B1 = 35(1 - 1) = 0
For n = 2, B2 = 35(2 - 1) = 35 and so on.
Thus all whole number multiples of 35 are present in set B.
Thus every member of set A is present in every member of set B but at least one member of set B is not present in set A.
Hence, option (a).
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