Let U denote the set of all senators in Congress and let D  =  {x U | x is a Democrat} R  =  {x U | x is a Republican} F  =  {x U | x is a female} P  =  {x U | x is a physician}. Write the set that represents each statement. (a) The set of all Democrats who are female or are physicians a. D ∩ (F ∩ P) b. D ∩ (F ∪ P)     c. R ∪ (F ∪ P) d. D ∪ (F ∩ P) e.R ∩ (F ∪ P) (b) The set of all senators who are not Democrats or are physicians a. Dc ∪ P b. Dc ∩ P  c. R ∩ P d. (D ∪P)c e. (D ∩ P)c

Q: Let A,B,C,D be set. Prove that (A x B) \ (C x D) = [(A\C) x B] or [A x (B\D)] Kindly Indicate the…

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Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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Q: Let A and B be finite sets with A - B = {a, b, c, d, e, f, g} and An B = {h, i, j, k, l, m}. Find…

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Q: Which of the following pairs of sets can be placed in a​ one-to-one correspondence?   a.​ {1,2,3,4}…

A: A ​one-to-one correspondence of sets –     If each element is paired with exactly one element from…

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

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Q: Prove or give a counter example, let A and B be sets. Then P(A∪B) = P(A)∪P(B)

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Q: List the set in roster form. C=​{z​| z is an odd integer greater than 21 and less than or equal to…

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Q: Express the set in roster form. B = (x | XEN and x is a multiple of 7)

A: For given set B we have to write it in roster form.

Q: Let A, B, and C be sets. Is the following equality true or false? A x (BUC) = (A × B) U (A × C')

A: Sets, distributive law

Q: Let U denote the set of all employees at Universal Life Insurance Company, and let T  =  {x  U | x…

A: T∪C=x:x∈T or x∈CT=x∈U|x drinks teaC=x∈U| x drinks coffeeT∪C=x:x drinks tea or coffee           =the…

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: Let A = {H, T} be the set of outcomes when a coin is tossed, and let B = {1, 2, 3, 4, 5, 6} be the…

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Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: Q26. Which subset immediately precedes the subset {X7, X5, X3, X2, X1} of the set S= {X7, X6, X5,…

A: Total number of subset of S =2^8 = 256 Now let's find subsets having 5 elements. {x7,x6,x5,x4,x3}…

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A: a)If sup A and sup B exists then          supA∪B=max{sup A,sup B} So supA∪B exists. First option is…

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: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

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Q: Find

A: First we write U as universal set. Then find complement.

Q: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x |  9 − x…

A: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | 9 − x =…

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

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Q: Find the intersection of the sets. {r, e, a, l}∩{l, e, a, r}

A: Given:A=r,e,a,lB= l,e,a,rIntersection set:The set containing all elements of A that also belong to…

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: (LP4) Here are two definitions about sets: Let A be a set. The set A is called the compliment of A…

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Q: Let U= { 1,2,3,...,20}. Let A, B, C be the subsets of U. Let A be the set of all numbers, which are…

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Q: Write out in words the description of the set. {x|x  , x ≤ 10} The set of        , x, such that x…

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Q: Let U = {1, 2, 3, 4, 5} be the universal set. Let A = {1, 2, 3}, B = {1, 3, 5}, and C = {2, 4, 5}.…

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Q: A = {2, 5, 6}, B = {1, 2, 3, 7}, C = {x|x € Z, x > 0, x < 10}, D = {10, 11} a. Write out An B b.…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.