2. For this problem, let the universal set U ={1,2,3,..,20}, and A = the elements of U that are congruent to 3, mod 4. (Remember that the absolute value symbols are used to indicate cardinality, or number of elements. And B is the complement of B, meaning the elements of U that are not in B. Hint: draw a Venn diagram!) Suppose that B is a subset of U such that |A| = |B| and A U B = 11 Then find |A n B| . Explain your reasoning in detail.

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Q: Find the cardinality of the following set. В %3D {3, 6, 9, 12, 15, 18, 21, 24}

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Q: Let *' be defined on the set N. Which of the following are both commutative and associative?

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Q: (a) Suppose that we choose three subsets of M such that each of them con- tains 100 elements, the…

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Q: 16. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25} ;B={-5,0,1,2,3,4,5};…

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Q: Determine the cardinality of each of the following sets. a. A x B, where A = {a, b, c, d, e}, B…

A: a) A=a,b,c,d,e, B=xb) a,b,cc) d) Φ,Φ,Φ,a,

Q: Consider the set S= {x €N|x is odd and 10<x<30}. Determine the cardinality of the power set of s.

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Q: Suppose that A and B are disjoint finite sets. Prove that AUB is finite.

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Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

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Q: 10. The supremum of a non-empty set S, if it exists, is always unique.

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Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: 1. Let set U = {n | n E whole numbers, 10 10 and c < 30}; BC C; CCU. Answer all the following…

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Q: The Venn diagram here shows the cardinality of each set. Use th set. 8 3 11

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Q: 11. consider the following sets: U = {-5,–4, –3, –2, –1,0,1,2,3,4,5}, A = {x: x² = 25}, B =…

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Q: 8. Use the Venn diagram to the right to determine the cardinality. U A B n(A U B) three five nine 12…

A: Venn diagrams

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Q: is the cardinality of the set {characters in set A}?

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…

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A: Introduction :

Q: Show that Z has the same cardinality as the set E of even integers.

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Q: Consider the following sets: U= {−5, −4, −3, −2, −1,0,1,2,3,4,5}, A = {x : x^2 = 25}, B = {−5,…

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only…

Q: . consider the following sets: U = {-5,–4,–3, – 2, –1,0,1,2,3,4,5}, A = {x: x² = 25}, %3D CTY B =…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.