Mark each statement True or False. Justify each answer. (a) If s n → 0, then for every ε > 0 there exists N ∈ N such that n ≥ N implies s n (b) If for every ε > 0 there exists N ∈  such that n ≥ N...

Mark each statement True or False. Justify each answer.

(a) If s_n
→ 0, then for every ε > 0 there exists N ∈ N such that n ≥ N implies s_n

(b) If for every ε > 0 there exists N ∈
 such that n ≥ N implies s_n
<>_n
→ 0.

(c) Given sequences (s_n) and (a_n), if for some s ∈
, k > 0 and m ∈ N we have | s_n
– s | ≤ k | a_n
| for all n > m, then lim s_n
= s.

(d) If s_n
→ s and s_n
→ t, then s = t.