Question

Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D ,...

  1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D , i.e. the set of all subsets of D .
  1. How many elements are there in P(D) ? Prove it!
  1. Which number is greater: the number of different subsets of D which contain the digit 7 or the number of different subsets of D which do not contain the digit 7? Explain why!

  1. Which number is greater: the number of different subsets of D which contain more than five digits from D (like {0,1,2,5,7,9} or D itself) or the number of different subsets of D which contain less than five digits from D (like {3,4,6,8} or ∅ )? Explain why!
Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D,...
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D, i.e. the set of all subsets of D.    a) How many elements are there in P(D)? Prove it!    b) Which number is greater: the number of different subsets of D which contain the digit 7 or the number of different subsets of D which do not contain the digit 7? Explain why!    c) Which number is greater: the number of different...
Let S be a finite set and let P(S) denote the set of all subsets of...
Let S be a finite set and let P(S) denote the set of all subsets of S. Define a relation on P(S) by declaring that two subsets A and B are related if A and B have the same number of elements. (a) Prove that this is an equivalence relation. b) Determine the equivalence classes. c) Determine the number of elements in each equivalence class.
A subset of a power set. (a) Let X = {a, b, c, d}. What is...
A subset of a power set. (a) Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }? comment: Please give a clear explanation to what this set builder notation translate to? Because I've checked the answer for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}}. I don't understand because the cardinality of A has to be 2 right? Meanwhile, the answer is basically saying there's 6 elements. So...
Thus, A + (B + C) = (A + B) + C. If D is a...
Thus, A + (B + C) = (A + B) + C. If D is a set, then the power set of D is the set PD of all the subsets of D. That is, PD = {A: A ⊆ D} The operation + is to be regarded as an operation on PD. 1 Prove that there is an identity element with respect to the operation +, which is _________. 2 Prove every subset A of D has an inverse...
Answer the following brief question: (1) Given a set X the power set P(X) is ......
Answer the following brief question: (1) Given a set X the power set P(X) is ... (2) Let X, Y be two infinite sets. Suppose there exists an injective map f : X → Y but no surjective map X → Y . What can one say about the cardinalities card(X) and card(Y ) ? (3) How many subsets of cardinality 7 are there in a set of cardinality 10 ? (4) How many functions are there from X =...
Given a random permutation of the elements of the set {a,b,c,d,e}, let X equal the number...
Given a random permutation of the elements of the set {a,b,c,d,e}, let X equal the number of elements that are in their original position (as listed). The moment generating function is X is: M(t) = 44/120 + 45/120e^t + 20/120e^2t + 10/120e^3t+1/120e^5t Explain Why there is not (e^4t) term in the moment generating function of X ?
Let S denote the set of all possible finite binary strings, i.e. strings of finite length...
Let S denote the set of all possible finite binary strings, i.e. strings of finite length made up of only 0s and 1s, and no other characters. E.g., 010100100001 is a finite binary string but 100ff101 is not because it contains characters other than 0, 1. a. Give an informal proof arguing why this set should be countable. Even though the language of your proof can be informal, it must clearly explain the reasons why you think the set should...
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the...
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the two statements (i) ∀x ∈ A, [P(x)∨Q(x)] and (ii) [∀x ∈ A, P(x)]∨[∀x ∈ A, Q(x)]. Argue whether (i) and (ii) are (logically) equivalent or not. (Can you explain your answer mathematically and by giving examples in plain language ? In the latter, for example, A = {all the CU students}, P(x) : x has last name starting with a, b, ..., or h,...
(complexity theory): let language C be: C = {<p,n> | p and n are natural numbers...
(complexity theory): let language C be: C = {<p,n> | p and n are natural numbers and there is no prime number in the range [p,p+n]} a)explain if the given explanation is good, or if it is bad, explain why: a professor wanted to prove that language C belongs to class NP like this: "for each word <p,n> that belongs to C, there is a confirmation that proves its belonging to the language: the confirmation is formulated by a non...
Activity 10.5. Suppose A is a set that definitely does not contain any cats, and let...
Activity 10.5. Suppose A is a set that definitely does not contain any cats, and let f:P(A)→P(A∪{Grumpy Cat}) represent the function defined by f(X)=X∪{Grumpy Cat} (a) Verify that f is injective. (b)Verify that f is not surjective. (c) Describe specifically how to restrict the codomain of f to make it bijective. restricting the codomain the “induced” function X→B created from function f:X→Y and subset B⊆Y by “forgetting” about all elements of Y that do not lie in B, where B...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT