Something is combustible when it can react with air and heat to create a fire. Something is flammable when it can react with air and heat **at typical temperatures** and **easily** create a fire. For instance, a log is combustible, but not flammable, as it takes quite a bit for the log to catch fire at normal temperatures. Paper is combustible and flammable because it can catch fire easily at normal temperatures. Gasoline is also flammable, as liquid gasoline rapidly evaporates at normal temperatures and catches fire very easily.
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