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.

Q: Do A = {1,2,3, 4,...} and B = {-1,0,1,2, 3, 4, ...}have the same cardinality? O No because elements…

A:

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

A: According to the given information, it is required to show that the two given sets have equal…

Q: 2. Exactly one of the following statements is true for all sets A, B,C. Draw a Venn diagram for the…

A: This is the proof of DeMorgan's law.

Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: Consider the sets A {r|a E Z,-2<r < 2} {2) C = {1,3, 5, 9, 11} D = {-2, –1,0, 1, 2} E = {a, b, c, d,…

A: topic - sets

Q: What is the cardinality of the set D = {x | x is a letter in the word "apple"}?

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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: 2 of 4 02 (Core): I can represent a set in roster notation and set-builder notation; determine if an…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 3. If A is a set, and |A| represents the cardinality of A, then use the definition of set A has the…

A: To prove that the set [1,2) has the same cardinality as the set [3,∞), we need to establish a…

Q: Now, your turn! Activity 1. Answer what is asked. 1) Name the elements of the following sets. al A…

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Q: In the universal set of U = {English words}, here’s three sets: • A = {gem, rue, cat, roof} • B = {w…

A: That's easy. Have a great day!!!

Q: Show that the setA={1/5,1/9,1/13,1/17, ...} has cardinal number א0 by establishing a one-to-one…

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Q: Find the cardinal numbers of the sets in the given pair to determine whether the sets are…

A: n(T) and n(P) represents the number of elements in the sets T and P respectively. Obtain the values…

Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: 1. Let U = {1,3,5,..., 17, 19} be the universal set, A = {3,7, 11, 15, 19} and B = Determine the…

A: Given: Universal set: We have to determine the following

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”.