Prove or disprove each of the statements below.\\
(A) (4 marks) Let $f : \mathbb { R } ^ { 2 } \longrightarrow \mathbb { R }$ be a continuous function that takes both positive and negative values. Then $f$ has infinitely many zeros.\\
(B) (6 marks) Let $f : \mathbb { R } \longrightarrow \mathbb { R } ^ { 2 }$ be a continuous function. Then $f$ is not open.