  In this paper we consider finite conditional random quantities and
conditional previsions assessments in the setting of coherence. We use a
suitable representation for conditional random quantities; in particular the
indicator of a conditional event $E|H$ is looked at as a three-valued quantity
with values 1, or 0, or $p$, where $p$ is the probability of $E|H$. We
introduce a notion of iterated conditional random quantity of the form
$(X|H)|K$ defined as a suitable conditional random quantity, which coincides
with $X|HK$ when $H \subseteq K$. Based on a recent paper by S. Kaufmann, we
introduce a notion of conjunction of two conditional events and then we analyze
it in the setting of coherence. We give a representation of the conjoined
conditional and we show that this new object is a conditional random quantity.
We examine some cases of logical dependencies, by also showing that the
conjunction may be a conditional event; moreover, we introduce the negation of
the conjunction and by De Morgan's Law the operation of disjunction. Finally,
we give the lower and upper bounds for the conjunction and the disjunction of
two conditional events, by showing that the usual probabilistic properties
continue to hold.
