Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise connected sets.

Q: Let A, B and C are sets. Prove that <= is transitive

A: For proving transitivity we need to show that if A&lt;=B and B&lt;=C then A&lt;=C

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: Let A,B,C and D are any sets then prove: If A C C and B c D then A U B CCUD.

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Q: Find an example of nonempty, distinct sets A, B, C for which (ANB) UC = (AUB) nC.

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Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: 5. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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Q: Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser…

A: We used the concept that if a set contains n elements then it power set contains 2n elements .

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: Prove that if A is transitive set, then A+ is also a transitive set.

A:

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

Q: . Let A and B be two connected subset

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

Q: Consider S to be the universal set. Let X = (AUB) nC and Y = (AnT)U (An B). %3D Write out the…

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Q: Đ A is a closed set.

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Q: If A C BỊ U B2 where B1 and B2 are disjoint open sets and A is compact, show that An B1 is compact.…

A: To Show- If A ⊆ B1 ∪ B2 where B1 and B2 are disjoint open sets and A is compact, show that A ∩ B1 is…

Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: Q.A. Is the nonnepatbe orthaut t. a cohvek set?

A: Answer is negative

Q: 4.2. Let S be the open set consisting of all points z such that |2| < 1 or |z – 2| < 1. Show that S…

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

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

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Q: & and X are open sets.

A:

Q: A set is not open if its complement is not closed. O True O False

A: To find the given statement is true or false .

Q: Suppose that A and B are disjoint finite sets. Prove that AUB is finite.

A: Here are given sets A and B are finite sets. Then A=m, B=n  where m, n any fixed positive integer.…

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

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

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Q: The empty set o is open set ylgn O İhi O

A: See the detailed solution below.

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: The empty set o is open set

A:

Q: Prove that A-B = A iff A intersection B = null set

A: From the given information it is required to prove that:

Q: Let A be a finit set and let |p(A)|=n. Let B = A U {x} for some x∉B, How many subsets does B have…

A: Let A be a finite set with m elements Then number of elements in p(A) has 2melements Given p(A) =…

Q: Let A and Bbe finite sets satisfying |A|= 9, B| = 6 and |An B = 2. Calculate the following: () |AUB…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Consider the following theorem of set theory: For any two sets A, B, [A U (B – A)] = A U B. a.…

A:

Q: The empty set is open set ylgn O İhi O

A: The complement of an empty set is the whole set, which of course contains everything including all…

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

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Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

A: Let A, B, and C are sets. Now we prove that A∪B∩C and C-A∪B∪(B-(A∪C)) are disjoint.

Q: Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly.

A: 3 Given A is any set. We have to prove that A is also a set. Since, A is any set Then as every set…

Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

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Q: Use a Venn diagram to determine if the pair of sets are equal. S. S'nT and (SUT')' II III IV

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: 4. Prove that the set Z is a closed set in R.

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Q: 5. State whether each of the following statements is true or false, in either case substan- tiate/…

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Q: Draw a venn diagram to represent the set A insersects B, but B has a line over it showing its a…

A: To represent the given combination of sets (A intersection B complement) in a Venn diagram

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: 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: ndary of a path-connected set in R^2 with the usual

A: We have to check that boundary of a path connected set in R2 with the usual topology is…

Q: Prove that a set A is connected iff A is and interval.

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Q: Let A and B be sets. Define precisely (but concisely) what it means for A to be a subset of B

A: Let, A and B be setswhat it means for A to be a subset of B.

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: