15 Let A and B be contented sets with B negligible. Apply Proposition 2.7 with 4to show that A U B is contented with A u B D(A U B) D(A)(B). 15 Let A and B be contented sets with B negligibl...

Question

Question

Answer 1

Answer #1

by general rule

$v(A \cup B) = v(A) + v(B) - v(A \cap B)$

a special case arises of A and B are disjoint,

$(A B)$ is negligible

$(A \cap B) = v(\O ) = 0$

by addition rule for disjoint sets

$(A \cup B) = v(A) +v(B)$

Answer 2

Similar Homework Help Questions

paita vi an aamissiDie Tunction are admissible. 2.3 If D is the set of discontinuities off:P-A, show that the set of discontinuities of pA is contained in D u BA (a 2.4 If A and Bare contented se...

paita vi an aamissiDie Tunction are admissible. 2.3 If D is the set of discontinuities off:P-A, show that the set of discontinuities of pA is contained in D u BA (a 2.4 If A and Bare contented sets with A e B, apply Proposition 2.5 with f-Pa-PaPa, g ps to show that paita vi an aamissiDie Tunction are admissible. 2.3 If D is the set of discontinuities off:P-A, show that the set of discontinuities of pA is contained in D...
8. Let A and B be subsets of some universal set U. From Proposition 5.10, we...

8. Let A and B be subsets of some universal set U. From Proposition 5.10, we know that if A S B, then B S A. Now prove the following proposition: For all sets A and B that are subsets of some universal set U, A C B if and only if B S A.
Proposition 4.1: Here is the question: Proposition 4.1. Let (E,E. u) be a measure space. Then...

Proposition 4.1: Here is the question: Proposition 4.1. Let (E,E. u) be a measure space. Then the following holds for all measurable sets A, B and A, A2,.. (we do not require them to be disjoint): (Finite additivity): AnB = 0 (AUB) /(A)ja(B), (Monotonicity): A C B u(A) < i(B) (A) (Sequential continuity): An A >u(An) If u(A1) and A,\A, then u(An)/(A) (U An) < E1 4(An). (Boole's inequality): fa Give an example of a measure space where the second...

(7) 15 ptsl Let Y - a +bX +U, where X and U d b are...

(7) 15 ptsl Let Y - a +bX +U, where X and U d b are are randon variables and a an constants. Assume that E[U|X] 0 and Var u|X] - X2. (a) Is Y a random variable? Why? (b) Is U independent of X? Why? (c) Show that Eu0 and Var[uEX2] (d) Show that E[Y|X- a bX, and that E[Y abEX]. (e) Show that VarlyX] = X2, and that Varly-p?Var(X) + EX2].
(5) Let A, B and C be sets. Show that there is a bijection between the sets F(A, B x C) and F(A, B) x F(A, C) (5) Let A, B and C be sets. Show that there is a bijection between the sets F(A, B x...

(5) Let A, B and C be sets. Show that there is a bijection between the sets F(A, B x C) and F(A, B) x F(A, C) (5) Let A, B and C be sets. Show that there is a bijection between the sets F(A, B x C) and F(A, B) x F(A, C)
#9-11 please 9. Let A and B be disjoint sets in the universe U. Let C...

#9-11 please 9. Let A and B be disjoint sets in the universe U. Let C be a proper subset of A. (a) Draw a Venn Diagram representing this information. (b) What is BAC? 10. Let A be a set in the universe U. (a) Draw a Venn Diagram and shade in the region A. Then draw another Venn Diagram with the same set A, but shade in A'. (b) What is A'U A? 11. Give an example of three...

please help with these A B and U are Sets An Byn U = (An B...

please help with these A B and U are Sets An Byn U = (An B ) u U = ? Let A = {-1, -3,3,1}, B = {0,2,3,4} and let U = {-3,-1,0,1,...,4} be the universal set
Let A and B be two sets. (a) Show that Ac = (Ac ∩ B) ∪...

Let A and B be two sets. (a) Show that Ac = (Ac ∩ B) ∪ (Ac ∩ Bc ), Bc = (A ∩ Bc ) ∪ (Ac ∩ Bc ). (b) Show that (A ∩ B) c = (Ac ∩ B) ∪ (Ac ∩ Bc ) ∪ (A ∩ Bc ). (c) Consider rolling a fair six-sided die. Let A be the set of outcomes where the roll is an odd number. Let B be the set of outcomes...
Let A, B, C be three sets. Show that A ∪ B = A ∩ C...

Let A, B, C be three sets. Show that A ∪ B = A ∩ C ⇐⇒ B ⊆ A ⊆ C.

(discrete math) i need help with sets 15. Let A={1,3,5,7,9), B - {3,6,9), C= {2,4,6,8) and...

(discrete math) i need help with sets 15. Let A={1,3,5,7,9), B - {3,6,9), C= {2,4,6,8) and U - {1,2,3,4,5,6,7,8,9). Find: a. AUB b. AnB And e. A-B f. P(B)