If D is an event space (probability domain), and each of A and B is in D, then s

Question

If D is an event space (probability domain), and each of A and B is in D, then show that A U B is in D.

Here's the definition of probability domain for reference: The statement that D is a probability domain means that D is a collection of sets such that each of the following statements are true:

i) There is a set I in D such that if A is in D, then A is a subset of I.

ii) There is a set O in D such that if A is in D, then O is a subset of A.

iii) If A is in D and B is in D, then A (intersect) B is in D.

iv) If A is in D, then there is a set A' (reads A Hat, which means everything not in A but also include O) in D such that A (intersect) A' = O and A U A' = I.

Explanation / Answer

if you equate each subset with an event, this may help answer a) & b) for c) consider any element in A U B, it must be in either A or B

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.