19. For all sets A, B, and C, if AC BandACC then AC BnC.

Q: 5. For the set C = {4, 5, 6, ....} is it true or %3D false that 7 e C? True False

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

Q: State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram…

A: The formula for The principle of inclusion and exclusion  for three sets A |A\cup B \cup C| = |A| +…

Q: 6. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Determine which of these…

A: Solve the above question.

Q: What can you say about the sets A and B if A ⊕ B = A?

A: The symmetric relation is described as, A ⊕ B =(A-B) U (B-A)

Q: (5) If possible, give an example af each af foll o ing la) Sets A,B and c Snch that As B, B$ C A CC.

A: Here we have to solve 5(a) and 5(b) We have to give an example about the given condition.

Q: Express (4, 10) as a set {x : |x – al < c} for suitable a and c.

A:

Q: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

A:

Q: Suppose that A and B are sets. A is a subset of X and B is also a subset of X. Please teach me how…

A:

Q: Let Aand B be non-empty sets such that |A|>|B|.If the number of elements in A∪Bis atmost 42 and at…

A: Let the number of elements in A is a , hence, |A|=a . Let the number of elements in B is b , hence,…

Q: Use Venn diagram to shade in region of following sets: a) An(BUT) b)

A:

Q: exactly how many subsets does set B={1,2,3,4} have

A: The given set is

Q: Suppose that A= {a,b,c,d} Then |A| =.?

A: Let X be a set , then X be number of elements in set X

Q: The inter setion of infuite opeh sets need notto bo oPen.

A: The given problem is to show that the intersection of infinite open sets need not to be an open set.

Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

Q: 14. A set SCR is closed if and only if S'CS.

A:

Q: For all sets D, E and F, if D- FCE-F then DUF CEUF.

A:

Q: 3. For the set C = {4, 5, 6, ..} is it true or false that 4 E C? True False

A: We have to check

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: If Set A = {M,I,C,H,A,E,L} and Set B = {J,O,R,D,A,N}, what is A ⋃ B?

A:

Q: Prove: Va,b,ce Z, if a|b and a|c then a|(b-c)

A: ab  &amp;  ac This means that b &amp; c are multiples of a. ⇒b=a·k  &amp;  c=a·m     where k, m∈Z

Q: 2) Explain how you count the number of elements in the set A = {n EN| n <500 and gcd (n, M) = 1},…

A:

Q: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

A:

Q: Let A = {a,b,c,d} be the set containing the four elements a, b, c and d. Let S = {X |X is a subset…

A: Sets

Q: Consider sets A={1,3,5} and B = {2,4,6}. find A ∩  B

A: We apply the property of intersection

Q: 1. Which of the following sets are equal? А 3D (а, b, с, d} C = {d, b, a, c} В 3 [d, е, а, с) D =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are  red

Q: Deter mine al subset relationships, amang the sets {1,2,3, 4? , {2.4,63, {2,4}, {X€NI<<63,Ø

A:

Q: Consider sets A={1,3,5} and B = {2,4,6}. Find A U B

A: The given sets are A={1,3,5} and B = {2,4,6}. The union of any two sets is the set of all the…

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: Express (4, 10) as a set {x: Ix - al&lt; c} for suitable a and c.

A:

Q: 1. Are the two sets (An B)UC and A - (Bn C) the same set? Use Venn Diagram shadings to prove your…

A: As per our Bartleby guidelines, we are allowed to answer one question per query, Please ask Q2 as a…

Q: 98how' that the Set cwith the o perations

A:

Q: 15. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25}…

A:

Q: Let A = {a, a, b, c} and B = {a, b, c}. Prove that A = B. Thus, the number of times an element is…

A: Given A={a,a,b,c} and B={a,b,c} we  have to show that A=B, for  this we will show that A⊂B and B⊂A…

Q: 1. If A ana B are sets, show that Ac B if and only if An B = A.

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

Q: (4.1) For sets A and B. prove that P(AB) = P(A)~P(B).

A:

Q: 2. Draw a Venn diagram for the set AU(BnC).

A: We first draw U, A, B, C

Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1…

A: a) If 1 and 7 are adjacent then we consider 1,7 as one number.  It can be 17 or 71. 2 ways. When 1,7…

Q: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: Show that the set EE is: (ii). Closed iff E¯=E

A: Show that the set E is Closed iff E¯=E

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: 4. Suppose A = {a, b, c, d} and B = {1, 2}. Write out the following sets (а) А х В (b) AUB (с) A ПВ…

A: Given: A=a, b, c, d and B=1,2.

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is: