note: If one of the antecedents is singular and the other plural, as in the second example, put the plural one last to avoid awkwardness.
exception: If one antecedent is male and the other female, do not follow the traditional rule. The sentence Either Bruce or Elizabeth should receive first prize for her short story makes no sense. The best solution is to recast the sentence: The prize for best short story should go to either Bruce or Elizabeth.