Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A ⊆ B ⊆ X I have a problem proving this... Can anyone please prove this for me? Thank you very much.

Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A ⊆ B ⊆ X I have a problem proving this... Can anyone please prove this for me? Thank you very much.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Let B={x∈R|x5∈Q} be a set. Is B countable? Justify the answer by showing the explicit formula for…

Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

Q: I don't understand why you put Ui element of I. I think you made a mistake. Please let me know.…

A: Step 1:Step 2:Step 3:Step 4:

Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

Q: Use an element argument to prove the following statement.. Proof: For all sets A, B, and C, An (B-C)…

Q: Let A, B and C be any sets (subsets of some universal set U). Use the choose-an-element method to…

A: Two sets A and B are said to be equal if the following hold: A⊆BB⊆A To prove identities that…

Q: Let A, B, and C be subsets of a universal set U and suppose n(U)= 150, n(A) = 22, n(B) = 24, n(C) =…

Q: 1. Let A = {a, x, c) and B = {b, x, d}. Write down an element of each of th following sets: (a) (An…

Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: Suppose A and B are finite sets with |A| = a, |B| = b and |An B| = c. Find (a) |AB| (b) AX (AUB)|…

Q: Prove that for all sets A and B, A – B = AN B

Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

Q: (1) If A is an uncountable (2) Z† × Z is a countable set. Select one of the following choices: set…

A: A countable set is a set that can be put into one-to-one correspondence with the natural numbers…

Q: Give a proof by contrapositive of the following statement: "Let A and B be sets. If An B = A, then…

Q: F oranges pineapples bananas apples pears V peas carrots beans corn potatoes

Q: Let U be the universal set with disjoint subsets A and B, where n(U) = 37, n(A) = 8, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law A'∩B' =…

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following - T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Prove that if X ∩ Y = X ∩ Z and X ∪ Y = X ∪ Z, then Y = Z for all sets X, Y , and Z.

Q: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

Q: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element We are using here if x €A. <=>…

Q: Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

Q: Let A, B and C all be sets with a universal set U. Prove or disprove the following statements: i. If…

A: Let's prove or disprove each statement:i. If B⊆C then (A×B)⊆(A×C):Proof:Assume B⊆C. Let (x,y) be an…

Question

Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A ⊆ B ⊆ X

I have a problem proving this... Can anyone please prove this for me? Thank you very much.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

It's not asking to prove it's a subset. It's asking to prove it's a bejection.
Consider the following statements about subset relations between sets: i. N ⊆ Z ii. R ⊆ N iii. Z⊆R Which of them are true? (a) Only (ii)(b) Both (i) and (ii) (c) Both (i) and (iii) (d) All of the above Which of the following statements are true? (Select all the choices that apply) (a) |N|=|Z| (b) |N|<|Z| (c) |Z|=א0 (d) |R|>|Z| Which of the following statements are tautologies? (Select all the choices that apply) (a) P → Q (b) P ∧ ¬P (c) P ∨ ¬P (d) P → P The contrapositive equivalency of ¬Q → P is given by: (a) P → Q (b) Q → P (c) ¬P → Q (d) ¬Q→P
When |S| denotes the number of elements of the set S, and S = {x/1 ≤ x ≤ 100, x € integer } There are three subsets of S, namely sets A, B and C. It is known |A|=(10+k), |B|= (7+2k), |C|= (8+2k), |A∩B|=(2+k), |A∩C|=(3 +k), |B∩C|=2k, |A∩B∩C|=k and |(AUBUC)'|=40 Draw the Venn diagram, determine the value of k ? Determine the number of elements of each set A, B and C?
(4) Let A, B, C be subsets of a universal set U. Determine if the following statements are true or false. If true, prove them. If false, find a counterexample. (a) An(B\C) = (A \ B) n (A \ C) (b) If Ac C BC, then AC B. (c) (ANB) UC = (AUC) n(BUC).
I need help with this
is the textbook missing a line? should this statement be inserted? "if no member of the set is smaller than m, but there is at least one member that is smaller than.... why or why not?