Determine the equivalent sequnces-boundness and cauchy

Question

Problem:Equivalent sequnces: boundness and Cauchy

1. Show that if (a_n)^∞ _n=1 and (b_n)^∞ _n=1 are equivalent sequences of rationals, then  (a_n)^∞ _n=1 is a Cauchy sequence if and only if (b_n)^∞ _n=1 is a Cauchy sequence.

2. Let ε > 0. Show that if (a_n)^∞ _n=1 and (b_n)^∞ _n=1 are eventually e-close, then (a_n)^∞ _n=1 is bounded if and only if (b_n)^∞ _n=1 is bounded.