### Understanding the Power Set of a SetThe concept of a power set is fundamental in the study of set theory, a branch of mathematical logic. The power set of any given set \( S \) is the set of all possible subsets of \( S \), including the empty set and \( S \) itself.#### Question:**What is the power set of \( \{ \emptyset, \{ \emptyset \} \} \)?**#### Multiple Choice Options:1. \( \{\emptyset, \{\emptyset\}, \{\{\emptyset\}\}, \{\emptyset, \{\emptyset\}\} \} \)2. \( \{\emptyset\} \)3. \( \{\emptyset, \{\{\emptyset\}\}\} \)4. \( \{\emptyset, \{\emptyset\}, \{\{\emptyset\}\}, \{\emptyset, \{\emptyset\}\}, \{\{\emptyset\}, \{\emptyset\}\} \} \)### Explanation:For the set \( S = \{ \emptyset, \{ \emptyset \} \} \):- The empty set, \( \emptyset \), is always a subset of any set.- \(\{ \emptyset \} \) is a subset.- \(\{ \{ \emptyset \} \} \) is also a subset.- The original set itself, \(\{ \emptyset, \{ \emptyset \} \} \), is also a subset.Therefore, the elements that should appear in the power set are:- The empty set: \( \emptyset \)- The subset containing the empty set: \( \{ \emptyset \} \)- The subset containing the singleton set of the empty set: \( \{\{ \emptyset \} \} \)- The original set itself: \( \{ \emptyset, \{ \emptyset \} \} \)Thus, the power set is:\[ \{\emptyset, \{ \emptyset \}, \{\{ \emptyset \} \}, \{ \emptyset, \{ \emptyset \} \} \} \]The correct answer is:1. \( \{\emptyset, \{\emptyset\}, \{\{\emptyset\}\}, \{\emptyset, \

To find power set of A={∅,{∅}} To avoid confusion, let us start with A={x,y}A={x,y}. The power set…

Answered: The power set of {0, {0}} is O {0, (0),…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Format Requirement Algorithms in pseudo code MUST be placed in code blocks/fences, and use either the cpp or java syntax highlighter. Algorithms should follow the pseudo code standard described in handout 1. Your pseudo code should be placed in a code block, for example Algorithm alg_name(a, b) { // A description of the algorithm // input: a - a positive decimal integer; b - an integer // ouput: the sum of a and b c = a + b // or, c <- a + b return c } Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmath.pdf Ways enter into the math mode in Notion: https://www.notion.so/help/math-equations
Use C language to write a program
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Must be new solution and run on GNU Common Lisp! Using Lisp, write a program that solves the Missionaries and Cannibals problem that uses a DFS( depth first search). It should use (mac start end). Start is the current state (which can be (3 3 l) and End is the goal state (which can be (0 0 r). This should output the sequences of moves needed to reach the end state from the start state. This should print nil if there is no solution. For example, the call should be something like this! Call: (mac '(3 3 l) '(0 0 r)) Output: ((3 3 l) (2 2 r) (3 2 l) (3 0 r) (3 1 l) (1 1 r) (2 2 l) (0 2 r) (0 3 l) (0 1 r) (1 1 l) (0 0 r))
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The power set of {0, {0}} is O {0, (0), {{0}}, {0, {0}}} 0 {0} ○ {0, {0}} {0, {0}, {0, {0} }, { {0}, {0}}}