Given that \(A_n=2^n-1\) for all integers \(n \geq 1\)

Quantity A

The unit digit of \(A_{26}\) = Unit's digit of (\(2^{26} - 1\))

Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2

So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 26 by 4 and check what is the remainder
=> 26 divided by 4 gives 2 remainder
=> \(2^{26}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{26}\) = 4

=> Unit's digit of \(2^{26} - 1\) = 4 - 1 = 3

Quantity B

The unit digit of \(A_{34}\) = Unit's digit of (\(2^{34} - 1\))

34 divided by 4 gives 2 remainder
=> \(2^{34}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{34}\) = 4

=> Unit's digit of \(2^{34} - 1\) = 4 - 1 = 3

Clearly, Quantity A(3) = Quantity B(3)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to find Unit's digit