Define sets A and B as follows: A = {n €Z|n= 8r - 3 for some integer r} and B = {m €Z|m = 4s + 1 for some integer s}. Is A CB? Is B C A?

Q: The following data reflect the number of defects produced on an assembly line at an electronics…

A: Reviewing information, X : No. of defects produced on an assembly line…

Q: Use the union rule to answer. If n(A) = 6, n(B) = 11 and n(An B) = 5, what is n(A U B)? n(A U B) =

A:

Q: 6. 3c2 - 5c for c = 3 76 8. 5a 3b + 5 for a = 4 andb 3 %3D

A: To find the values of the given expressions (6) 3c^2-5c at c=3 (8)5a-3b+5 at a=4 and b=3.

Q: given n (A⋂B) = 18, n (A) = 3, n (B) and n (A⋂B) = 2.Find n (B) and the number of subsets of set B

A: Solution

Q: For the set ?={−3,0,57,−8‾√,2.314520968724609....,14}A={−3,0,57,−8,2.314520968724609....,14}.…

A: Given :A=-3,0,57,-8,2.314520968724609...,14To indentify those that are…

Q: Fill in the missing element of B such that A = B. A = {7, 19, g, #, 2, 4, &, f, 17, 1, k} B = {#,…

A:

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: Use the given information to find n(A x B) and n(B x A). n(A) = 33 and n(B) = 4 Find the number of…

A: If we have two sets A, B such that  the cardinality of A =m and, the cardinality of B =n then, the…

Q: (d) D= {n €Z:n −3} (e) E = {}\{}

A: Here we have to find the set D and E in list form.

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

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

A:

Q: Prove: If (where b + 0 and d + 0), then C + d d a + b

A: Consider the given information, If ab=cd then show that a+bb=c+dd. First we consider ab=cd.

Q: Is the following statement true or false? {0} ⊂ {0}

A: given that                                                    {0}⊂{0} we have to check is the…

Q: ample. A oB indep, How about their are

A: We know : If two events are independent than occurrence of one does not effect the probability of…

Q: If n(A) = 106, n(A ∪ B) = 141, and n(A ∩ B) = 46, find n(B).

A:

Q: Use the given information to find n(A× B) and n(B × A). n(A) = 67 and n(B) = 4 Find the number of…

A: Note:- Cartesian product of two sets is obtained by pairing each element of first set with each…

Q: If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M).…

A:

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: n(A) = 104, n(A ∪ B) = 144, and n(A ∩ B) = 45, find n(B).

A: The following information has been given: n(A) = 104, n(A ∪ B) = 144,  n(A ∩ B) = 45 We need to…

Q: Find, if possible, (a) AB and (b) BA.

A: (a) Consider the given matrices A and B. As the number of the rows is equal to the number of columns…

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: Prove. all sets A,B and C, (a) (A-B)- C = CA-C)-B disprove each of the following for or

A: We Know that A - B means elements of A which are not the elements of B. i.e.      A - B = {x : x ∈ A…

Q: 11. For all sets A, B, and C, AN (B-C) C (A N B)– (A N C).

A: We use basic formula of set theory like A – A = Ø  B – A = B⋂ A’ B – A = B – (A⋂B) n(AUB) = n(A – B)…

Q: Use the union rule to answer the question. If n(A n B) = 8, n(A U B) = 34 and n(A) = 32, what is…

A: We know,      n(A U B) = n(A) + n(B) - n(A ∩ B)      => n(B) = n(A U B) + n(A ∩ B) - n(A)

Q: Let A = {1, {b}, {1, b}} a. Place an e or in the blank to make each of the following statements…

A: ● Let x be an element of a set A , then its denoted as x∈A .● If All elements of a set B is present…

Q: Write the definition of A x B, where A and B are sets A x B = { }.

A: We want to define A x B

Q: Write the set {. . . , −7/8 , −3/4 , −1/2 , 0, 1, 3, 7, . . .} using set-builder notation.

A:

Q: B AUBNC: Au BNC: 12 6 6 17 13 U How many elements are contained in each of the following sets?

A: From the above venn-diagram, we have  U={6,10,11,12,13,17}. A={6,10,12,17}. B={6,12,17}.…

Q: Write out the following set by listing its elements between set brackets.( {r, s}^2 × {a} ) × {c, d}

A: The given equation to be solved is:

Q: Find the sets A and B if A − B = {1, 4, 7, 11}, B − A ={2, 20}, and A ∩ B = {3, 5 ,19}

A: Set Question

Q: If  n(A) = 69, n(B) = 23, and n(A ∩ B) = 3, find n(A ∪ B).

A:

Q: Given F= {-10, v-5, 1.567, 0, 20, v144}, identify the s a) whole numbers b) integers c) rational…

A: We have to find the following conditions according to the given information

Q: Find n(A) for the following set. A= the set of integers between -23 and 23

A: the given set A= the set of integers between -23 and 23the set builder form: A={x | x∈Z,…

Q: Let A = and B = . Find the following. а. 2А+B b. || A|| с. А о В

A: Vectors

Q: If a = (2, 4, – 1, 3) then ||-3a|l,= Select one: а. 30 b. -30 c. 27 d. -27

A:

Q: Use the following sets: A={Factors of 50} B={odd numbers} Which elements are found in A∩B?

A: A={Factors of 50} = { 1,2,5,10,25,50}  B={odd numbers} ={1,3,5,7,9,11,......}

Q: Find the following expressions if a = (6r, 0, r), b = (6s, –s, 7s), and c = (2t, 10t, 5). a ·b = 1.…

A: We need to find dot product.