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?

• A. Neither every member of A is in B nor every member of B is in A
• B. Every member of A is in B and at least one member of B is not in A
• C. Every member of B is in A.
• D. At least one member of A is not in B

Answer 1

The Correct Option is B

The correct answer is (B):
A=36n-35n-1 = 36n-1n-35n
Since an - bn 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.