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A “rival” is a person or organization with whom you are in an intense competition. This is often used in sports, where two teams are in more intense competition than usual. In American baseball, the Yankees and Red Sox are rivals. They are from two nearby cities and both have a history of excellence. They are rivals; their competition is more intense than normal. In basketball, you can say the same about the Los Angeles Lakers and the Boston Celtics.
In business, a company might have a rival in the same industry, one other company with which it has an intense competition. For years, Microsoft and Apple were rivals: they each had a different operating system, a different vision for the future. Both were competing for supremacy in personal computing.
Coca-Cola and Pepsi are rivals, so you would say: Pepsi is Coca-Cola’s rival, and Coca-Cola is Pepsi’s rival. You can say the same about Reebok and Nike, for example.
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