Question 1. 1. Use the operations in o-algebra, such as union, intersection, difference, countable union and countable intersection to generate the following intervals from intervals of the form (a,00), where a € R. a) [a, ∞) b) (-∞, a) c) (-∞, al d) [a, b] 2. Use the fact that the interval (a, ∞o) is measurable for all a € R to justify the measurabliity of intervals in (1).

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A: According to our guidelines we can answer only one question and rest can be reposted.

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A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

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A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. Use the operations in o-algebra, such as union, intersection, difference, countable unlöll and…

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