Investigate the following theorems (h) For sets A, B and C we have i. A\(B ∪...

Investigate the following theorems

(h) For sets A, B and C we have

i. A\(B ∪ C) = (A\B) ∩ (A\C),

ii. A\(B ∩ C) = (A\B) ∪ (A\C),

iii. A ̸= B if and only if (A\B) ∪ (B\A) ̸= ∅,

iv. A ∪ B ⊆ C if and only if A ⊆ C and B ⊆ C.

What happens in the extreme case(s) where some (or all) sets are empty?

Expert Solution

Colby Messinger answered 2 years ago

Suppose we have three sets of random variables Wh, Xi, and Yj (for h= 1,...,k, i=...

Suppose we have three sets of random variables Wh, Xi, and Yj (for h= 1,...,k, i= 1,...,m, and j= 1,...,n) all of which are mutually independent. Assume that the three sets of random variables are all normally distributed with different means but the same standard deviation. The MLE for the means are just the group means and the MLE for the variance is the mean of the squared errors of the observations from the groups when taking into account the...

A, B and C be sets. (a) Suppose that A ⊆ B and B ⊆ C....

A, B and C be sets. (a) Suppose that A ⊆ B and B ⊆ C. Does this mean that A ⊆ C? Prove your answer. Hint: to prove that A ⊆ C you must prove the implication, “for all x, if x ∈ A then x ∈ C.” (b) Suppose that A ∈ B and B ∈ C. Does this mean that A ∈ C? Give an example to prove that this does NOT always happen (and explain why...

(6ptseach)Let A={a,b,c},B={b,c,d},C ={b,c,e}. (a) Explicitly ﬁnd (i) A∪(B∩C), (ii)(A∪B)∩C, and (iii)(A∪B)∩(A∪C). (iv)Which of these sets are...

(6ptseach)Let A={a,b,c},B={b,c,d},C ={b,c,e}. (a) Explicitly ﬁnd (i) A∪(B∩C), (ii)(A∪B)∩C, and (iii)(A∪B)∩(A∪C). (iv)Which of these sets are equal? (b) Explicitly ﬁnd (i) A∩(B∪C), (ii)(A∩B)∪C, and (iii)(A∩B)∪(A∩C). (iv)Which of these sets are equal? (c) Explicitly ﬁnd (i)(A−B)−C and (ii) A−(B−C). (iii)Are these sets equal?

let A= {1,2} and C={8,9}. for each i=1,2, construct sets B sub i as well as...

let A= {1,2} and C={8,9}. for each i=1,2, construct sets B sub i as well as functions f sub i: A to B sub I, 1<=i<=4, with the following properties: 1) g sub 1 ° f sub 1 is onto C but f sub 1 is not onto B sub I. 2) g sub 2° f sub 2 is one-to-one but g sub 2 is not one-to-one.

Suppose we have three events, A, B, and C such that: - A and B are...

Suppose we have three events, A, B, and C such that: - A and B are independent - B and C are independent - P[AUBUC]=0.90 -P[A]= 0.20 - P[C]= 0.60 Compute P [C | AUB]

If I have two dice A and B, and I roll it twice, we have the...

If I have two dice A and B, and I roll it twice, we have the outcomes A1, A2, B1, B2. Let X = A1+ A2, Y= B1+B2. What is the probability of X+Y <= 22.

which of the following is an ionic compound a. H^2s b. NH^3 C. I^2 D. KI...

which of the following is an ionic compound a. H^2s b. NH^3 C. I^2 D. KI e.CCL^4 2. Which element has the following electron Configuration (Kr)5S^24D^105P^2? A. Sn b. Sb c. Pb D. Ge E. Te

Consider the following bivariate data. Point A B C D E F G H I J...

Consider the following bivariate data. Point A B C D E F G H I J x 0 1 1 2 3 4 5 6 6 7 y 5 5 6 5 4 3 2 0 1 1 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Calculate the covariance. (Give your answer correct to two decimal places.) (c) Calculate sx and sy. (Give...

Consider the following demand curve: A B C D E F G H I J P...

Consider the following demand curve: A B C D E F G H I J P $0.50 $0.45 $0.40 $0.35 $0.30 $0.25 $0.20 $0.15 $0.10 $0.05 QD 1 2 4 6 9 12 16 20 25 30 Calculate elasticities for pairs of points to check statements that were made during class and in the text. When making the calculations, use average price and average quantity for the two points. The formula for this should be in your notes. It is...

Prove the following Theorems: 1. A finite union of compact sets is compact. 2. Any intersection...

Prove the following Theorems: 1. A finite union of compact sets is compact. 2. Any intersection of compact set is compact. 3. A closed subset of a compact set is compact. 4. Every finite set in IRn is compact.

Question