For sets A and B we may define the set difference measure as |A_B| (the cardinality...

For sets A and B we may define the set difference measure as |A_B| (the cardinality of the set A-B), explain why this is never negative. We know this is not a distance, explain why and modify it so that it is a distance. Prove your claim (in particular be careful to show the triangle inequality holds)

Expert Solution

I hope you like this.

Colby Messinger answered 1 year ago

A= {{a}, a} p(A) = State the cardinality of set A & cardinality of p(A) ....

A= {{a}, a} p(A) = State the cardinality of set A & cardinality of p(A) . Please explain in great detail to provide a better understanding .

Cardinality State whether the following sets are finite, countable infinite or uncountable. Set of positive perfect...

Cardinality State whether the following sets are finite, countable infinite or uncountable. Set of positive perfect squares. Is it finite, countable infinite or uncountable? If it is countably infinite, set up the bijection between ℤ+. Negative numbers greater than or equal to -5. Is it finite, countable infinite or uncountable? If it is countably infinite, set up the bijection between ℤ+. Odd positive integers. Is it finite, countable infinite or uncountable? If it is countably infinite, set up the bijection...

Let X be a set with infinite cardinality. Define Tx = {U ⊆ X : U...

Let X be a set with infinite cardinality. Define Tx = {U ⊆ X : U = Ø or X \ U is finite}. Prove that Tx is a topology on X. (Tx is called the Cofinite Topology or Finite Complement Topology.)

Recognizing partitions - sets of strings. (b) Let A be the set of words in the...

Recognizing partitions - sets of strings. (b) Let A be the set of words in the Oxford English Dictionary (OED). For each positive integer j, define Aj to be the set of all words with j letters in the OED. For example, the word "discrete" is an element of A8 because the word "discrete" has 8 letters. The longest word in the OED is "pneumonoultramicroscopicsilicovolcanoconiosis" which has 45 letters. You can assume that for any integer i in the range...

show that the power set of N and R have the same cardinality

Using the set of scores below, determine if the difference between the two sets of scores...

Using the set of scores below, determine if the difference between the two sets of scores is significant at alpha .05, two tailed. Determine this through the paired t-test. Show the 5 steps of hypothesis testing. Solve manually, by hand showing all steps. Do not use SPSS or excel. X Y 3 8 8 7 5 6 7 7 6 6 8 9

Decide, with justification, if the following set properties are true for any sets A, B, and...

Decide, with justification, if the following set properties are true for any sets A, B, and C. 1. A∪(B∩C)⊆A. 2. A∪(B∩C)⊆B. 3. A ∩ B ⊆ A 4. B ⊆ A ∪ B 5. A ⊆ B ⇒ A ∪ B ⊆ B. 6. A ∪ B ⊆ B ⇒ A ⊆ B. 7. A⊆B⇒A∩B=A. 8. A ∩ B = A ⇒ A ⊆ B 9. A∩(B∪C)⊆A∪(B∩C) 10. A∪(B∩C)⊆A∩(B∪C) 11. A\(B∩C)=(A\B)∪(A\C)

Let (G,·) be a finite group, and let S be a set with the same cardinality...

Let (G,·) be a finite group, and let S be a set with the same cardinality as G. Then there is a bijection μ:S→G . We can give a group structure to S by defining a binary operation *on S, as follows. For x,y∈ S, define x*y=z where z∈S such that μ(z) = g_{1}·g_{2}, where μ(x)=g_{1} and μ(y)=g_{2}. First prove that (S,*) is a group. Then, what can you say about the bijection μ?

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?

A)Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of...

A)Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of S, where: Set A={3,4,9,10,11,13,18}A={3,4,9,10,11,13,18} Set B={1,2,4,6,7,10,11,12,15,16,18}B={1,2,4,6,7,10,11,12,15,16,18} LIST the elements in Set A and Set B: { } LIST the elements in Set A or Set B: { } B)A ball is drawn randomly from a jar that contains 4 red balls, 5 white balls, and 9 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) PP(A...

Question