How Do You Find The Difference Between Utility And Usefulness?

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Zem, regarding your "utility program", you could easily write "Its utility will be to wake you up". The two terms "utility" and "usefulness" have no difference in meaning, except the fact that "utility" is also a technical word used in economics and philosophy, amongst others, and hence can have a different connotation.
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Anonymous answered
Usefulness refers to which extent something is useful and the utility is the quality of that thing in practical use.

Both are inter-related terms. In other words you can say that utility is a part of usefulness term. Usefulness  means having practical utility of a thing which is beneficial, pertinent and functional.

For example you have a utility program that wakes you up in the morning. It's usefulness will be to wake you up at exactly the same time you would want.

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