For each n ≥ 0 define binary strings a _n and b _n as follows: a ₀ = 0, b ₀ = 1, and for n > 0 , a _n = a _n−1 b _n−1 ; b _n = b _n−1 a _n−1

1. Show that for every n ≥ 0, an and b _n have the same length

2. Show that for every n ≥ 0, an and b _n differ in every position

3. Show that for every n ≥ 0, a _2n and b _2n are palindromes