I've been making my way through the new Kunen and I've come across an exercise that I can't work out. The question is this:
Let $\kappa$ be a singular cardinal. Show that there is a collection $A$ of $\kappa$ many two-element subsets of $\kappa$ such that no element of $[A]^\kappa$ forms a $\Delta-$ system. Where $[A]^\kappa$ is the set of subsets of A of size $\kappa$.
Any help would be appreciated (i.e. hints welcome).