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

A:

Q: If Si and S2 are convex sets, is their union S1 U S2 a convex set. Explain your answer.

A: The union of two convex sets is not convex.

Q: 2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum,…

A: Let, mA = min {x : x ∈ A}        mB = min {x : x ∈ B}   Now, let m = min{mA , mB} Then, m = mA if mA…

Q: For two sets, X and Y , if  X ∩ Y = ∅ , then which of the following is true? Choose one answer and…

A: Given that For two sets, X and Y, X∩Y=∅ To find which of the following statement is true:

Q: Describe the sets of points in space whose coordinates satisfy the given inequalities. a. x2 + y2 +…

A: Inequalities are given by(a)x2+y+z2≤64(b)x2+y2+z2>49

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: what is the product of two sets? B.) What does this mean? Can you give an example?

A: Concept: In set theory product of two set A and B means cartesian product which is represented by…

Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: Classify the relationship(s) between the two following sets: A = {Mike Evans, Russell Shepard,…

A: A = {Mike Evans, Russell Shepard, Lavonte David, Gosder Cherilus, Joe Hawley} B = {Russell Shepard,…

Q: Determine if each statement is true or false. 1. If A not equal to B then A ∩ B = empty set. 2. If…

A: we will be using basic set theory to answer these questions

Q: True OR False For And Justify 22 = {YERM: YTA=bTy=0} A € Rmxn 2 is Convex Set, Constrant set V fixed…

A:

Q: Given the following​ sets, find the set left parenthesis Upper A prime intersect Upper B right…

A:

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: 2}

A:

Q: Which of the following sets, given by the roster method, is equal to the set below given in…

A: The objective of the question is to find the set that matches the set-builder notation {x belongs to…