Consider whether the following statements are true or false: a. The intersection of any two convex sets is convex. b. The union of any two convex sets is convex. c. The difference of a convex set A from another convex set B is convex.

Q: Prove that for any sets A, B, C: (AUB)-B A - B

A:

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

A:

Q: • Show that if D is a set and E is a closed set containing D, then E must contain ƏD, i.e., the…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

A:

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: Indicate whether the following sets are equal. A={x, j, a, w}, D={x, a, b, y}

A: The given two sets are, A=x,j,a,w and D=x,a,b,y By definition, The two sets A and B are equal sets…

Q: If A, B,C, and D are sets, does it follow that (A ⊕ B) ⊕ (C ⊕ D) = (A ⊕ C) ⊕ (B ⊕ D)?

A: The symmetric difference between the set is associative and commutative. So, (A⊕B) ⊕C=A⊕(B⊕C)…

Q: Prove that intersection of any class of convex subsets of N is convex?

A:

Q: If c eR and S is a set, define cS be a convex set and suppose c > 0 and d > 0. Prove that cS + dS =…

A:

Q: AAB = (A\ B) U (B\ A). Prove or disprove: (1) (2) (AAB) (AAB)° (AUB) \ (ANB) A¢AB° %3|

A:

Q: Define the sets A, B, C, D, and E as follows: • A = {x €R:x 2} ' = {x € R: |x| < 2} • C = Do the…

A: A = x∈IR : x&lt;-2B = x∈IR : x&gt;2C = x∈IR : x&lt;2A = x∈IR : x&lt;-2⇒x∈(-∞ , -2)A = (-∞, -2)B =…

Q: 4. Consider the drawing below: C. Write a paragraph that explains why the following proposition is…

A: Given,          A circle is shown below :

Q: Which of the following statements on sets is FALSE? O a. AN A° = Ø O b. Equivalent sets are equal. O…

A:

Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your answer…

A:

Q: 2. Given A, B, and C are non-collinear points, draw the following or explain why it is impossible…

A: We have given three points A,B,C  which are non colinear  that  is these three points does not lie…

Q: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

A:

Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

A:

Q: Which of the following sets are open, and which are closed? Explain your answers by sketching the…

A:

Q: Let A=(0, π ) υ (π e?] %3D c. Is A a closed set? d. Does A contain any isolated points? е. Find the…

A:

Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: Determine if the following statements are true or false. Here A represents any set. (a) oCA (b) A'CA…

A: Here let us consider A to be any set which consists some elements U is a universal set  A' is a…

Q: _1. It is a pictorial representation of the relationships between sets wherein the sets are…

A: Since you have posted multiple questions. We will solve first question. If you want the other…

Q: Decide whether the following propositions are true or false.If the claim is valid, supply a short…

A: A compact set is always closed and bounded.

Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your answer…

A: Consider the given Venn diagram, which is given in the question. From the Venn diagram…

Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: • Show that if D is a set and E is a closed set containing D, then E must contain ðD, i.e., the…

A:

Q: Three sets are defined as follows: A = {x: 0 ≤ x ≤ 4} B = {x: 0 ≤ x ≤ 3} C = {x: −1 ≤ x ≤ 2} Draw…

A:

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: 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: Suppose that A and B are two sets such that n[A]= 5, n[B]= 9, and n[A U B]= 13. If n[U]= 19, then…

A: The given values are nA=5,nB=9, and nA∪B=13. Also nU=19.

Q: Can you conclude that A = B if A, B, and C are sets such thata) A ∪ C = B ∪ C? b) A ∩ C = B ∩ C?c) A…

A: According to the given information, it is required to conclude that A = B if A,B,C are sets such…

Q: When using Venn diagrams to verify or determine whether set statements are equal we use…

A: Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements…

Q: What is the union of sets A and B?

A: Assume the independent sets A and B. Set A = 0,1,2Set B = 4,5,6

Q: If X = {u,v} what is the power set of X? (in answering this question, use {} as the null set, and do…

A:

Q: Construct the intersection graph of the following collection of sets: A - (0.±2,+4. 16. 18....)

A:

Q: Prove that the following statements are EQUIVALENT: For any sets A and B, a. ACB b. AnB = A C. AUB=B

A:

Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: The intersection of sets A and B is denoted by which of the following?(a) A ∩ B (b) A ∪ B (c) A ⊆ B…

A: Sets are represented as the collection of different objects . There can be a finite set or an…

Q: Without graphing, determine which of the followingdata sets are exactly linear, approximately…

A: You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y…

Q: Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.…

A: The union of two sets contains all the elements contained in either set (or both sets). The…

Q: Let A, B, and C be sets. Does A – C = B – C imply A = B? If so, prove it. If not, give a…

A: We have to give a counter example for  A – C = B – C imply A = B.

Q: Refer to the following Venn diagram, and list the points that belong to each set. (Enter your U A •y…

A:

Q: What will be the cartesian product of three sets if one set of them is empty?

A: The answer is given as follows:

Q: Let S1, S2, S3 be convex sets. Is their intersection nS, necessarily a convex set If 'yes' show, if…

A: A set S is convex if the line segment joining any two points lies in S That is  A set S is convex if…

Q: Consider the two sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is…

A: Given :               The sets A = a,e,i,o,u   and B = c,m,n,r,s,v,w,x,z

Q: we defined the symmetric difference of sets A and B to be A AB = (A U B) – (A n B) = (A – B) U (B –…

A: The proof of associative law for symmetric difference is given as follows

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: