Question:
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?
- Neither every member of A is in B nor every member of B is in A
- Every member of A is in B and at least one member of B is not in A
- Every member of B is in A.
- At least one member of A is not in B
Correct Answer: 2
$A=36^{n}-35 n-1=36^{n}-1^{n}-35 n$
Since $a^{n}-b^{n}$ is divisible by a $-b$ for all positive integral values of n, A is a multiple of 35 for any integral value of n and B is a set containing all the multiple of 35 including 0.
Hence, every member of A is in B but not every element of B is in A.
$A=36^{n}-35 n-1=36^{n}-1^{n}-35 n$
Since $a^{n}-b^{n}$ is divisible by a $-b$ for all positive integral values of n, A is a multiple of 35 for any integral value of n and B is a set containing all the multiple of 35 including 0.
Hence, every member of A is in B but not every element of B is in A.
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