5 You are given that \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\) are odd functions, defined for \(x \in \mathbb { R }\).
- Given that \(\mathrm { s } ( x ) = \mathrm { f } ( x ) + \mathrm { g } ( x )\), prove that \(\mathrm { s } ( x )\) is an odd function.
- Given that \(\mathrm { p } ( x ) = \mathrm { f } ( x ) \mathrm { g } ( x )\), determine whether \(\mathrm { p } ( x )\) is odd, even or neither.