In (a)-(d), state whether the equation is an identity (valid for all \(\mathbf{F}\) or \(f\) ). If it is not, provide an example in which the equation does not hold.
(a) \(\operatorname{curl}(abla f)=\mathbf{0}\)
(b) \(\operatorname{div}(abla f)=0\)
(c) \(\operatorname{div}(\operatorname{curl}(\mathbf{F}))=0\)
(d) \(abla(\operatorname{div}(\mathbf{F}))=\mathbf{0}\)