Quantitative Aptitude – Modern Maths – Set Theory – If A = {6^2n -35n -1: n = 1,2,3,…}

Slot -2 – Quantitative Aptitude – Modern Maths – Set Theory – If A = {6^2n -35n -1: n = 1,2,3,…}

 If A = {6^2n -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: b) Every member of A is in B and at least one member of B is not in A.

Solution:
Given, A = 36^n – 35n – 1 = 36^n – 1^n – 35n
Since a^n – b^n is divisible by a – b for all positive integral values of n, So 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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