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Important information about Rings : Ideals

Let S be a subset of a set X. Let R be the ring of real-valued functions on X, and let I be the set of real-valued functions on X whose restriction to S is zero. Show that I is an ideal in R.

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Ideals are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.