I've just started studying belief bases and I am struggling to understand how the relevance postulate for contraction guarantees minimality.
(Relevance) If q ∈ A and q ∉ A ÷ p, then there is a set A′ such that A ÷ p ⊆ A′ ⊆ A and that p ∉ Cn(A′) but p ∈ Cn(A′∪{q}).
But, for example, for $A = \{p \land q \}$. I'd think that a contraction A ÷ p that allows only minimal change would, at least, be A ÷ p = {q}. But this contraction, from my understanding, doesn't satisfy relevance, since there's no A′ such that {q} ⊆ A′ ⊆ $\{p \land q \}$.
What am I missing?