Answer these questions for the poset ({2,4,6,9, 12,18, 27. 36, 48,60, 72},|). a) Find the maximal elements. b) Find the minimal elements. c) Is there a greatest element? d) Is there a least element?

Q: 2. Use an edge-counting argument to show that K, cannot be drawn on a 2-holed torus without edges…

A: Suppose K9 had a 2-cell embedding in the torus. Then, this embedding has v=9 vertices and…

Q: What set is in another class of infinity that is bigger than R?

A:

Q: Which sets are compact? The set of natural numbers less than some number M

A: We know that a set is compact if and only if it is closed and bounded. The set of natural numbers…

Q: Identify the following set as finite or infinite. x|x is a rational number smaller than 3} Chooro

A: Given set { x | x is a rational number smaller than 3}

Q: An architect designing a parking lot has a row 62.0 m wide to divide into spaces for compact cars…

A: We need to formulate a system of linear equations using the scenario. We also need to solve the…

Q: Decide with a proof that the set Nk is countable or not, where N is the set of natural numbers and k…

A: According to the given information it is required to proof that the set

Q: Use double set inclusion to prove that dep. PANB) = P(A)n P(B).

A: The problem is related with power set P of sets. Here, we have to show that P A ∩ B = P A ∩ PB using…

Q: Show that if a and b are positive integers, then there are divisors c of a and d of b with (c, d) =…

A: image is attached

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

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

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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: For circuit M, find out what orders its nonzero ones have elements and find their divisors of zero,…

A:

Q: Use the definition of oubset to prove : If A,B,C are set then ((BnA) -c) U ((Bnc) -A)) CCOUA)

A:

Q: The set of numbers in the form , where a and b belong to the set in Exercise 8 and b # 0, is called…

A: Rational numbers are represented in the form of pq where q≠0.

Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

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Q: 3 10. Show that R² span

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Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(2, 1,−2)T, (−2,−1,…

A:

Q: Can a set and it's Complement be both nowhere dense in R? A Ac=R-A

A:

Q: The pattern​ 1, 8,​ 27, 64,​ 125, ... is a cubic pattern named because 1equals=1times•1times•1 or 1…

A: The given series is 1, 8, 27, 64, 125, … are the cubed values of 1, 2, 3, 4, 5, … respectively.

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: Use the roster method to list the elements in the set: {x|x is a negative integer greater than -5}.

A: Our Aim is to list the element in the set: x|x is a negative integer greater than -5using Roster…

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: In Exercises 7–8, use the roster method to list the elements in each set. 7. {x|x is a natural…

A: Given: 7. xx is a natural number less than 38. xx is an integer greater than -4 and less than 2 To…

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

A:

Q: Suppose ACB and BCC. Show that = {A, B-A, C-B} is a partition of C.

A:

Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: Determine n(U), the number of elements in the universal set, given n(X) = 47 and n(X′) = 156.

A: Note : {X, X'} forms a partition of U. i.e. X & X' are disjoint and their union is the universal…

Q: Which of the following are minimal elements of the partially ordered set {2, 3, 4, 5, 6, 7, 8, 9, .…

A: Find which are minimal elements of the partial order set 2, 3, 4, 5, 6, 7, 8, 9, … ordered by…

Q: Is the set named empty, finite, or infinite? {points on a line} {baseballs used in a major league…

A: A set is empty if there is no element in it. A set is finite if there are countable elements in it.…

Q: 2. Use the element method of proof to prove that for all sets A, B, and C, (An B) -CCANC.

A:

Q: Select the regions that correspond to the set AN BNC°.

A:

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

A:

Q: 33, A Sphene has the iengen of t

A:

Q: Given a set has m members, where m=15, how many proper subsets are there?

A:

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: Find an increasing subsequence of maximal length and a decreasing subsequence of maximal length in…

A: GIVEN CLEAR EXPLANATION BELOW

Q: Is the following set connected: V = {(x, y) € R² | 1<x² + y² <4}? Briefly justify your answer.

A: Connected set:- If any two points of a given set can be joined by a continuous polygonal arc such…

Q: Prove in any Pythagorean triple (a, b, c) that either a or b is divisible by 3 and one of a, b, c is…

A: A Pythagorean triple is three numbers a,b,c such that a2+b2=c2. Also if a,b,c is a Pythagorean…

Q: Show that if A is a countable set, and B CA is infinite, then B is countable. [Hint: How could we…

A: To prove that  If A is a countable set and B is a subset or equals to A is infinite then B is…

Q: C. Think of a set with m + n elements as composed of two parts, one with m elements and the other…

A: m+n elements as composed of two parts.

Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

A:

Q: If i and i are in R™, then –i is in span {ū, 3}. |

A:

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: Suppose the universal set contains the natural numbers that are no more than 20. Sets A and B are…

A:

Q: Compute the first 5 Legendre polynomi als , ..., L, (x), (These Solutions, P,x) , where n is a whole…

A:

Q: Is the set named empty, finite, or infinite? a) N = {counting numbers} b) V {vowels} {points in the…

A: The empty set (or null set) is a set that has no members.   Finite sets are the sets having a…

Q: In drawing 3 CD’s from a lot, defective and non defective CD’s , let A, B , C and D mean at least…

A: let A, B , C and D mean at least one Defective CD, at least one non defective CD, 2 defective CD’s…

Q: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

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”.