For any positive integer x, let xR be the integer whose binary representation is the reverse of the binary representation of x. (Assume no leading 0s in the binary representation of x.) Define the function R+ : N−!N where R+(x) = x + xR.

a. Let A₂ = {〈x, y〉| R⁺(x) = y}. Show A₂ ∈ L.

b. Let A₃ = {〈x, y〉| R⁺(R+(x)) = y}. Show A₃ ∈ L.