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Let A be the set {1, 2, 3, 4}, and P(A) be the power set of A. a. Find | P(A)|. b. List all of the elements SEP(A) such that |S| = 3.

Let A be the set {1, 2, 3, 4}, and P(A) be the power set of A. a. Find | P(A)|. b. List all of the elements SEP(A) such that |S| = 3.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Power Sets and Combinations** In this section, we explore the concept of power sets and how to determine specific subsets. Consider the set \(A = \{1, 2, 3, 4\}\). The power set, denoted as \(\mathcal{P}(A)\), represents all possible subsets of \(A\). ### Tasks **a. Find \(|\mathcal{P}(A)|\):** The power set of a set with \(n\) elements contains \(2^n\) subsets. For the set \(A\), which has 4 elements: \[ |\mathcal{P}(A)| = 2^4 = 16 \] **b. List all elements \(S \in \mathcal{P}(A)\) such that \(|S| = 3\):** We are interested in subsets of \(A\) that have exactly 3 elements. These subsets are combinations of 3 elements chosen from the 4 elements in \(A\). The subsets are: - \(\{1, 2, 3\}\) - \(\{1, 2, 4\}\) - \(\{1, 3, 4\}\) - \(\{2, 3, 4\}\) These are the elements of \(\mathcal{P}(A)\) that contain exactly 3 elements.
Transcribed Image Text:**Power Sets and Combinations** In this section, we explore the concept of power sets and how to determine specific subsets. Consider the set \(A = \{1, 2, 3, 4\}\). The power set, denoted as \(\mathcal{P}(A)\), represents all possible subsets of \(A\). ### Tasks **a. Find \(|\mathcal{P}(A)|\):** The power set of a set with \(n\) elements contains \(2^n\) subsets. For the set \(A\), which has 4 elements: \[ |\mathcal{P}(A)| = 2^4 = 16 \] **b. List all elements \(S \in \mathcal{P}(A)\) such that \(|S| = 3\):** We are interested in subsets of \(A\) that have exactly 3 elements. These subsets are combinations of 3 elements chosen from the 4 elements in \(A\). The subsets are: - \(\{1, 2, 3\}\) - \(\{1, 2, 4\}\) - \(\{1, 3, 4\}\) - \(\{2, 3, 4\}\) These are the elements of \(\mathcal{P}(A)\) that contain exactly 3 elements.
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