5. Let A be a subset of 100, that is, A C {0, 1, 2, 3, ..., 98, 99} with cardinality 10. Show that there are always two different subsets X,Y C A such that the sum of the elements of X is equal to the sum of the elements of Y. (Hint: Recall Corollary 2 of Chapter 10, and use the pigeonhole principle.) Show that, moreover, X and Y can be chosen so that XnY= Ø, that is, so that X and Y don't share any element.

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: 5. Find Cardinality of the following set. (a) A= {r is an integer and 15 <I< 30} (b) A = {x is an…

A: Cardinality of set means total number of elements in the set.

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A: Suppose S is a set with cardinality n. Then power set of S contains 2n elements . Power set of any…

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A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 5. Use a floor or a ceiling function to find cardinalities of following sets: a) [{x € Z*]x is…

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Q: Select the following statements that are true. A and B are arbitrary sets. The cardinality of…

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Q: The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of each…

A: n(A) = number of elements in the set A   n(A∩C) = number of elements common in the sets A and B.…

Q: Suppose set A = {green, blue, red, black, orange} and set B = {gray, purple, blue, orange, white}…

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Q: Exercise 1. For any element x and set A, prove that the sets A and {x} × A have the same…

A: Result: Let A and B be any sets with the cardinality |A|=m and |B|=n, then the cardinality of A×B…

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Q: R.4. Prove that the set of real numbers in the interval (0, 1) which have a terminating decimal…

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Q: A set S is cardinally majorizable by a set T iff there exists a(n) from S to T.

A: Given: Let us suppose two sets be S and T. The set S is cardinally majorizable by the set T. We have…

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Q: R.2. Let S represent the set of positive integers that are perfect squares, and let C represent the…

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Q: (1) Let U = {1, 2, 3, ... , 9, 10} be the universal set. Let A = {x € U : x = 1 (mod 3)} and B = {x…

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Q: Indicate the cardinality of the set A, defined as the union of four sets of cardinalities 22, 31,…

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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: 2. For this problem, let the universal set U ={1,2,3,..,20}, and A = the elements of U that are…

A: U = {1,2,3,......,20} A = Elements of U that are congruent to 3 mod 4

Q: (a). Show that (0, 1) × (0, 1) and (0, 1) have the same cardinality. (Hint: shuffling two digit…

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