  In this paper sequent calculi for the classical fragment (that is, the
conjunction-disjunction-implication-negation fragment) of the nonsense logics
B3, introduced by Bochvar, and H3, introduced by Halld\'en, are presented.
These calculi are obtained by restricting in an appropriate way the application
of the rules of a sequent calculus for classical propositional logic CPL. The
nice symmetry between the provisos in the rules reveal the semantical
relationship between these logics. The Soundness and Completeness theorems for
both calculi are obtained, as well as the respective Cut elimination theorems.
