Determine which of the following statements are true and which are false. Prove the true ones and

Question:

Determine which of the following statements are true and which are false. Prove the true ones and provide counterexamples for the false ones.
a) If xn → ∞ and yn → -∞, then xn + yn → 0 as n → ∞.
b) If xn → ∞, then 1/xn → 0 as n → ∞.
c) If xn → 0, then 1 /x" →> ∞ as n → ∞.
d) If xn → ∞, then (l/2)xn → 0 as n → ∞.