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Which is it used in these examples ,the singular or the plural form?

e.g. The traveler and the local each has/have reason to love the beach.

Each traveler and each local has/have reason to love the beach.
Comments 
Each, everyone, every one, everybody require singular verbs.
Each traveler and (each) local has to love the beach.
But here
The traveler and the local each have reason to love the beach.
...the subject of the sentence is 'the traveller and the local', a plural subject.