  We consider a 2-valued non-deterministic connective $\wedge \hskip-5.5pt
\vee$ defined by the table resulting from the entry-wise union of the tables of
conjunction and disjunction. Being half conjunction and half disjunction we
named it platypus. The value of $\wedge \hskip-5.5pt \vee$ is not completely
determined by the input, contrasting with usual notion of Boolean connective.
We call non-deterministic Boolean connective any connective based on
multi-functions over the Boolean set. In this way, non-determinism allows for
an extended notion of truth-functional connective. Unexpectedly, this very
simple connective and the logic it defines, illustrate various key advantages
in working with generalized notions of semantics (by incorporating
non-determinism), calculi (by allowing multiple-conclusion rules) and even of
logic (moving from Tarskian to Scottian consequence relations). We show that
the associated logic cannot be characterized by any finite set of finite
matrices, whereas with non-determinism two values suffice. Furthermore, this
logic is not finitely axiomatizable using single-conclusion rules, however we
provide a very simple analytical multiple-conclusion axiomatization using only
two rules. Finally, deciding the associated multiple-conclusion logic is
coNP-complete, but deciding its single-conclusion fragment is in P.
