The conjunction \(P\land Q\), or \(P\) AND \(Q\), of two classical properties corresponds to the intersection \(\PC\cap\QC\) of the sets that represent them on the phase space, and the indicator for this set is the product \(P(\gamma)Q(\gamma)\) of the two indicator functions. What about the quantum case? In quantum logic \(P\land Q\) is identified with the intersection \(\PC\cap\QC\) of the two Hilbert subspaces, which is itself a subspace and thus a quantum property. The histories interpretation identifies \(P\land Q\) with the product \(PQ\) of the projectors \(P\) and \(Q\) provided the two projectors commute, that is, provided \(PQ=QP\). When and only when this condition is fulfilled is the product \(PQ\) itself a projector, and it projects onto the subspace \(\PC\cap\QC\), in agreement with quantum logic. However, if \(PQ\neq QP\) the conjunction \(P\land Q\) is undefined or meaningless in the sense that the histories interpretation assigns it no meaning. In the same way the disjunction \(P\lor Q\), the nonexclusive \(P\) OR \(Q\), is represented by the projector \(P+Q-PQ\) when \(PQ=QP\), but is otherwise undefined.