Explanation Given: For 6 children Mr. J brought 6 differently flavored jellybeans. Each child likes only certain flavors. A likes only chocolate, banana or vanilla and B likes only chocolate and banana. C likes only banana, strawberry and peach and D likes only banana and vanilla. E likes only chocolate and vanilla and F likes only chocolate, peach and mint. Concept used: Hall’s Theorem: The sequence of sets S 1 , S 2 , … , S n has a system of distinct representative if and only if I is a subset of { 1 , 2 , … , n } then the union of sets S i for i ∈ I contains at least as many elements as the set I has. Total number of subset I is 2 n . Proof: Consider that 6 children are denoted as A, B, C, D, E and F. There are 6 differently jellybeans as chocolate, banana, vanilla, strawberry, peach and mint. Consider that chocolate is denoted as 1, banana is denoted as 2, vanilla is denoted as 3, strawberry is denoted as 4, peach is denoted as 5 and mint is denoted as 6. It is given that A likes only chocolate, banana or vanilla, B likes only chocolate and banana, C likes only banana, strawberry and peach and D likes only banana and vanilla and E likes only chocolate and vanilla and F likes only chocolate, peach and mint, which can be written in the form of set as follows: As per the above information the sets formed are as follows: A = { 1 , 2 , 3 } B = { 1 , 2 } C = { 2 , 4 , 5 } D = { 2 , 3 } E = { 1 , 3 } F = { 1 , 5 , 6 } There are 6 sets A, B, C, D, E and F so, the value of n is 6. Total number of subset I is calculated as follows: 2 n = 2 6 = 64 Therefore, the set involve 64 subset of { 1 , 2 , 3 , 4 , 5 , 6 }

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Chapter 6.1, Problem 21E

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To show: That every child will not get a jellybean as per their taste.

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Chapter 6.1, Problem 20E

Chapter 6.1, Problem 22E

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Discrete Mathematics

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Let S1, S2, … , Sm and T1, T2, … , Tn be sequences...Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.2 - Prob. 1E Ch. 6.2 - Prob. 2E Ch. 6.2 - Prob. 3E Ch. 6.2 - Prob. 4E Ch. 6.2 - Prob. 5E Ch. 6.2 - Prob. 6E Ch. 6.2 - Prob. 7E Ch. 6.2 - Prob. 8E Ch. 6.2 - Prob. 9E Ch. 6.2 - Prob. 10E Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Prob. 13E Ch. 6.2 - Prob. 14E Ch. 6.2 - Prob. 15E Ch. 6.2 - Prob. 16E Ch. 6.2 - Prob. 17E Ch. 6.2 - Prob. 18E Ch. 6.2 - Prob. 19E Ch. 6.2 - Prob. 20E Ch. 6.2 - Prob. 21E Ch. 6.2 - Prob. 22E Ch. 6.2 - Prob. 23E Ch. 6.2 - Prob. 24E Ch. 6.2 - Prob. 25E Ch. 6.2 - Prob. 26E Ch. 6.2 - Find a graph in which a maximum matching has fewer...Ch. 6.2 - Prob. 32E Ch. 6.3 - Prob. 1E Ch. 6.3 - Prob. 2E Ch. 6.3 - Prob. 3E Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - In Exercises 5–10, a matrix is given with an...Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 21E Ch. 6.3 - Prob. 22E Ch. 6.3 - Prob. 23E Ch. 6.3 - Prob. 24E Ch. 6.4 - Prob. 1E Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - Prob. 5E Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - Prob. 14E Ch. 6.4 - Prob. 15E Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.5 - Prob. 1E Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6 - Prob. 1SE Ch. 6 - Prob. 2SE Ch. 6 - Prob. 3SE Ch. 6 - Prob. 4SE Ch. 6 - Prob. 5SE Ch. 6 - Prob. 6SE Ch. 6 - Prob. 7SE Ch. 6 - Prob. 8SE Ch. 6 - Use the independent set algorithm to find a...Ch. 6 - Prob. 10SE Ch. 6 - Prob. 11SE Ch. 6 - Prob. 12SE Ch. 6 - Prob. 13SE Ch. 6 - Prob. 14SE Ch. 6 - Prob. 15SE Ch. 6 - Prob. 16SE Ch. 6 - Prob. 17SE

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