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Which of the following statements is/are true?
I. ⌈x+n⌉=⌈x⌉+n\lceil x+n\rceil=\lceil x\rceil+n⌈x+n⌉=⌈x⌉+n for any real xxx and any integer n.n.n. II. ⌈x⌉+⌈−x⌉=1\lceil x\rceil+\lceil-x\rceil=1⌈x⌉+⌈−x⌉=1 if and only if xxx is not an integer. III. ⌈x⌉+⌈y⌉≤⌈x+y⌉≤⌈x⌉+⌈y⌉+1\lceil x\rceil+\lceil y\rceil\le\lceil x+y\rceil\le\lceil x\rceil+\lceil y\rceil+1⌈x⌉+⌈y⌉≤⌈x+y⌉≤⌈x⌉+⌈y⌉+1 for any real xxx and y.y.y.
What is the solution set to ⌈x3−8⌉=10?\lceil\frac{x}{3}-8\rceil=10?⌈3x−8⌉=10?
What is ⌈log559⌉?\lceil\log_{5}59\rceil?⌈log559⌉?
How many integers xxx satisfy the equation ⌈log3x⌉=4?\lceil\log_{3}x\rceil=4?⌈log3x⌉=4?
What is ⌈−π⌉?\lceil-\pi\rceil?⌈−π⌉?
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