Let S be a ring with ideals X and Y. Consider the subset X + Y = { x + y | x ∈ X, y ∈ Y} of S. Show that X + Y is an ideal of S.

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A: F→(x,y,z)=x3i→+y3j→+z3k→ Bounded b the solid x2+y2≤4,  0≤z≤4

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A: Note the following fact :  Conservative field : If F →=grad f ,then F→ is conservative .

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