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(a) State the definition of the cardinality of a finite set. (b) If A is a finite set with |A|= n, prove that |P(A)|= 2", where P(A) is the power set of A. (c) Let A be a finite set and let B be a subset of A with |A| = n, |B| Find a formula for the number of subsets of A that contain B and prove your statement. = m and 0 < m < n. (d) Prove the equality n 2n n n j=0

(a) State the definition of the cardinality of a finite set. (b) If A is a finite set with |A|= n, prove that |P(A)|= 2", where P(A) is the power set of A. (c) Let A be a finite set and let B be a subset of A with |A| = n, |B| Find a formula for the number of subsets of A that contain B and prove your statement. = m and 0 < m < n. (d) Prove the equality n 2n n n j=0

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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(a) State the definition of the cardinality of a finite set. (b) If A is a finite set with |A|= n, prove that |P(A)|= 2", where P(A) is the power set of A. (c) Let A be a finite set and let B be a subset of A with |A| = n, |B| Find a formula for the number of subsets of A that contain B and prove your statement. = m and 0 < m < n. (d) Prove the equality n 2n n n j=0
Transcribed Image Text:(a) State the definition of the cardinality of a finite set. (b) If A is a finite set with |A|= n, prove that |P(A)|= 2", where P(A) is the power set of A. (c) Let A be a finite set and let B be a subset of A with |A| = n, |B| Find a formula for the number of subsets of A that contain B and prove your statement. = m and 0 < m < n. (d) Prove the equality n 2n n n j=0
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