Weak decay iff or if strangeness changes?

Question

I know that for a decay if the strangeness changes then the decay is a weak decay because strangeness is conserved in both strong decays and electromagnetic decays. However, is it also true that if a weak decay occurs the strangeness must also change? i.e. do we have: $$\text{weak decay} \iff \Delta S\ne0$$ $$\text{or}$$ $$\text{weak decay} \Leftarrow \Delta S\ne0$$ If it is the latter, is their another necessary and sufficient condition (apart from looking at timescales) to see if a decay is weak?

Answer 1

No, a weak decay doesn't imply a change of $S$. For example, the decay of the neutron – the basic part of the beta-decay – has $S=0$ both in the initial and final state. So the first proposition is false and only the second one is true.