1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a counterexample.

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

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

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Q: 2. Classify each set as closed, open, or neither. Justify your answer. A= {-+:nEN} E. 1-:] [0, 1)

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Q: 4. Prove that, for any sets A and B, it is true that A C B iff AnB = A. Hint. There are two…

A: The intersection is a set operation. The intersection of finite number sets consists of elements…

Q: Consider two sets in ℝ² with the usual topology. Is the closure of a path-connected set also…

A: We will use knowledge of general topology to solve both the parts of this question. For the first,…

Q: Suppose that A is a Hintikka set. Then, for all terms s and t, s = t E A or ¬(s = t) E A

A: Given, Suppose that is a Hintikka set. Then, for all terms S and t,

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

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Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

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Q: d) Let X,Y, Z be sets. Calculate |XUYUZ if |X| = 50, [Y|= 90, |Z| = 71, |XnY| = 8, |Xn Z| = 9, |Yn…

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Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

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Q: Suppose that A and B are sets. Prove that A- B = AnB.

A: Suppose that A and B are set. Prove that A-B=A∩B¯.

Q: 4. In each case, sketch the closure of the set: 1 (c) Re (d) Re(z?) > 0.

A: Given:

Q: (4.2) For sets A, B and C, prove that (An B) x C = (A x C) n(B x C).

A: Here we have to prove that (A∩B)×C=(A×C)∩(B×C)

Q: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =B

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

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Q: 11 - Which of the following statement regarding sets is false I. AnA=A AUA = A A- (Bn C) = (A – B) U…

A: Union and intersection apply on same set gives the set itself

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: Disprove the following statement by finding a counterexample. For all sets A, B, and 6, C, An (BUC)…

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Q: - If C is Convex set ond a GR, then XC is a Convex set

A: Let C be a convex set and x∈R Then we have to show that xC is a convex set. The set xC is defined as…

Q: 4. By the use of Venn diagrams, in which the space C is the set of points enclosed by a rectangle…

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

A: Please check step 2 for the solution.!

Q: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = B?

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Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

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Q: 4. Prove that, for any sets A and B, it is true that A C Biff AnB = A. Hint. There are two…

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Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

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Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

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Q: .et A, B be any two sets. Prove that if A C B, then A n B = p.

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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: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

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Q: Let A, B, and C be sets. Prove that: Ax (B\C) = (A × B) \ (A × C).

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Q: Suppose A, B, and C are sets. Prove that (AU B) – C C AU (B – C). - -

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Q: 2. Determine if the following statements are true or false. Here A represents any set. (a) ¢ C A (b)…

A: Used simple logic to prove.

Q: Prove or disprove the following statement: Let A, B, X be sets. If X ⊆ A ∪ B, then X ⊆ A or X ⊆ B.

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Q: 1. Prove the following statements about sets A and B. A B= AN Bº %3D

A: Given: Let A and B be two sets. To prove,A-B=A∩Bc

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: 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: Show that if A and B are finite sets, then A ∪ B is a finite set.

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Q: Show that (B - A)U(C- A) = (BUC)- A 1) Using a Venn diagram 2) Using the definition of equal sets

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Q: O AC Biff P(A) C P(B).

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

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

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Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

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Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

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

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Q: If sets X and Y are uncountable, then prove or disprove that X-Y is uncountable.

A: Here we will prove or disprove the given statement.

Q: Show that the union of two sets, each of measure zero, has measure zero

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Q: Let A, B, and C be sets. Prove A × (B\C) = (A × B)\(A × C).

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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: