In each case determine whether the given set forms a M22 basis for If not, select the reason why not. GEEE)

Q: Exercise 16. Prove the above theorem. Hint: show A ∪ B = A ∪ B − (A ∩ B). Theorem 35…

A: To prove: A∪B=A+B-A∩B

Q: Disprove the following statement. For all sets A, B, and C of some universe U, (AAB)U (ANBNC) =…

A:

Q: Which of the following is not one of Euclid’s postulates?

A:

Q: Every fuzzy set A can be expressed as the union of all the fuzzy points which Belong to A O Non all…

A: Fuzzy set can have values which doesn't precisely meet the criteria but are approximately close.

Q: Give a basis for span(S), where S is the set given below. 1 1 -4 -2 -1 -5 -3 -2 9. -10

A: Given: S=1-2-3, 1-1-2, -459, 5-5-10 Objective of the given question is to find the basis of span(S)

Q: Exercise 2.21 Determine the  P (0/) (power of an empty set)

A:

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

A:

Q: Consider the set S:= {(z, y, 2) | 2. y.2 E {0, 1}} which is expressed in set-builder notation.…

A:

Q: If S is a ssubset of T , then u* (T) sµ* (S). ulgn O İhi

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

Q: QUESTION 5 Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C)U(B – C) by using…

A:

Q: 3. Consider the set X = which of the following is a basis for span(X) of Select one: stion a. 3. b.…

A:

Q: Given a set L sR", Following are true statements regarding conv L(convex hull of L):

A: In this question, we have to choose the correct option for the convex hull. the set L⊂Rn By using…

Q: Determine whether or not the set s ]日) 2 1. %3D 3. is a basis tor Rš.

A:

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one %3D such. If not, Why not exactly?

A: No, A≠{A} for any set A. Let  A=1,2,3 then number of elements in A are 3. Now,  A=1,2,3 here the…

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

Q: .

A:

Q: Show that the set K={a, b} with actions + and - defined tables   is a body whose zero element is a…

A: We are the set K={a, b} with actions + and ∙ defined in the following tables. Notice + operator…

Q: 9. If S and T are finite spanning sets for a vector space V, then S and I have the same number of…

A:

Q: |- Extends the set S={(-44,4} basis tor IR. to %3D

A: Basis of a vector space problem...

Q: Prove that if A is a set then so is {A}!

A:

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not ?

A:

Q: In Excrcises 9-18 mark each statcment True or Falsc (T/F). Justify cach answcr. 9. (T/F) If vi....…

A: As per company guidelines, we are supposed to answer only first question. Kindly ask others as…

Q: Let R(a, b, c), S(a, b, c), and T(a, b, c) be three relations. Write one or more Datalog rules that…

A: Given (R∪S)-T The solution for (R∪S) is as follows ∪(a,b,c)←R(a,b,c) OR S(a,b,c)--------(i) The…

Q: Let A, B sets such that AnB = An C. Prove that B = C

A: .

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly

A: Set equality

Q: EXERCISE 6.4 Define the binary ↑ (Sheffer's stroke), and its dual as follow xty10 :y x: 101 011…

A:

Q: Let A={2,4,6,...}, then A is well-ordered set ylgn ihi

A: Given a statement

Q: 10. Determine which sets are a basis for R². (a) (b) © {[2] [9] [17]} {8.8} (Ⓒ) {B} {[]+[2]}

A: To identify which of the given set is basis for R2

Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

A:

Q: Prove that if A and B are sets, then A - B = An BC.

A:

Q: if C={}         is {} subset of C ?

A: Question: Is the empty set a subset of itself?

Q: A topological space is said to be second countable if it has a countable basis. (a) Let R have the…

A:

Q: Prove that if A Cw is nonempty and UA = A, then A = w.

A: Given that, A⊆ω is non empty. And ∪A=A. To show A=ω it is enough to show that,  A⊆ω and  ω⊆A. One is…

Q: Let a and b be two elements in a lattice (A, ≤). Show that a ˄ b ˂ a and a ˄ b ˂ b if and only if a…

A: Suppose that a∧b<a and a∧b<b. To show that a and b are incomparable assume the contrary that a…

Q: If A is a subset of a me

A: Given is a matric space X and a subset A. Then it is needed to prove that  A=x: each open sphere…

Q: Let A,B be sets. Prove that AAB = if and only if A= B

A:

Q: A is subset of B if and only if A intersection B complement = phi

A: We have to show that given statement is true.

Q: et A = {a}

A: Given,        A = a

Q: Let A be a set. Show that ∅×A = A×∅ = ∅.

A: A×B=A×BIf A=∅ or  B=∅,thenA×B=A×B=0Since a set with 0 cardinality must be an empty set, we have…

Q: For every set A, {Ø} C A.

A: We use the definition of an empty set and subset of a set to answer the given question.

Q: Let A and Bbe seta Show hatAUB-U, hen ACB. e U a he ueal set

A:

Q: Consider the following: Let the universe of A and B be the set U. An B= AUBIF and only if A = B. A…

A: Solution by using properties of sets :

Q: Let U- lo, 1,2, 3,4,5,6,7,8,a}.let two fuzzy subsets A and B •f 0 be given by 2 3 4 6 7 8 9 0:2 0:3…

A: We have to find A∨B, A∧B, Ac, and Bc for the given data…

Q: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} Use the roster method to list the elements in the set A. A=

A: Given: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} The roster form is given by

Q: Let A and B be sets. Prove that (A − B) ∩ (B − A) = ∅.

A:

Q: Explain why the set is not a Basis. S = {(2,3), (6,9)}

A:

Q: Find the set A UØ. U= {1, 2, 3, 4, 5, 6} A=(3, 4, 5, 6}

A: Given, U=1, 2, 3, 4, 5, 6, A=3, 4, 5, 6