Universal quantification (ALL) is conjunctive and the existential quantifier (SOME) is disjunctive in the sense that ALL/Some can be replaced by a conjunction/disjunction of propositions involving constants.
The universal quantifier distributes over conjunction and the existential quantifier distributes over disjunction. That is,
- ALL(P and Q) = ALL(P) and ALL(Q)
- SOME(P or Q) = SOME(P) or SOME(Q)
However the universal quantifier fails to distribute over disjunction and the existential quantifier fails to distribute over conjunction. That is,
- ALL(P) or ALL(Q) => ALL(P or Q), but not vice versa
- SOME(P and Q) => SOME(P) and SOME(Q), but not vice versa