List of top Functional Analysis Questions on Banach Spaces and Completeness asked in GATE MA

Let \( X \) be the space of all continuously differentiable real valued functions on \( [0,1] \). Define the following norms on \( X \):
\[ p_1(x) = \sup\{ |x(t)| : t \in [0,1] \} \]
\[ p_2(x) = \sup\left\{ \left| \frac{d}{dt} x(t) \right| : t \in [0,1] \right\} \]
and \( p_3(x) = p_1(x) + p_2(x) \).
Which one of the following is TRUE?