7. Suppose A and B are sets and A is finite. Prove that A ~ B iff B is also finite and |A| = |B|.

Q: What set is in another class of infinity that is bigger than R?

A:

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

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: 4. Give an example of a non-measurable subset of R. (witheutProof)

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

A:

Q: Suppose that S is a non-empty finite set. Prove that ? has as many even-sized subsets as it does…

A: Let S be a non-empty set. Let A be the set of even sized subsets of S and let B be the set of odd…

Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

A:

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

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|.…

A:

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: (4.2) 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: S is a nonempty set of real numbers that is bounded.

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Q: d. What is the cardinality of a countably infinite set?

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Q: 2- Prove that H, is convex set.

A: Let us look at an arbitrary closed half-space defined as H+={x∈ℝn:aTx-b≥0}, representing a half…

Q: 6. Every finite set in R is compact. Why?

A: The given question is related to real analysis. We have to show that every finite set in ℝ is…

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: 3. is in the span of the set { -1 Birini seçin: O Doğru O Yanlış

A:

Q: the set of students at your school who either are not sophomores or are not taking discrete…

A: Given: Suppose that A is the set of sophomores at the school and B is the set of students in…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

A:

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: Suppose that X and Y are sets such that the power set of Y is a subset of the power set of X. Does…

A:

Q: Suppose A and B are sets. Prove that A – B = AN B.

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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…

A:

Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

Q: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A:

Q: uppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either…

A: Given: To explain the given statement as follows,

Q: Show by membership that for all sets A, B and C: А - (AnB) CА - В

A:

Q: 10. The supremum of a non-empty set S, if it exists, is always unique.

A: We need to prove that Supremum of a non empty set S, if it exists, is always unique.

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: 3. Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

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

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

A:

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: If geRla,b] and if h(w)= gcu) encept %D finite number f points for [a, b],'then and in of prove that…

A: First we have to divide the set into finite subsets of x intervals required.

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

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Q: (3.2) Indicate which of the following sets are compact in X. (a) C = {4,n € N}, X = R (b) C = Qn (0,…

A:

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: let A Set bounded belou, erove that C. inf A Inf C A ン

A:

Q: 7. Suppose that a set X is equipped with the finite closed topology. Which one of the followings is…

A: As per the policy, we are solving first question. Please repost the question and specify which…

Q: 3. Prove that if A is a set then so is {A} but do NOT use an argument that involves stages…

A: Let A is any set then as every set is a subset of itself then, A⊆A⇒A∈PA⇒A∈PPA

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

A:

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

A:

Q: Suppose that A is the set of sophomores at your school and B is the set of students in discrete…

A: We use set theory here: A: The set of sophomores at your school B: Set of students in discrete…

Q: Let A, B, C be arbitrary finite sets from the same universal set U. - (a) Is it true that A - B C (A…

A: SOLUTION-

Q: Ifs is(finite or infinite) Contable Set then prove that M*(S) ==

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Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .

Q: 4. Use a proof by contrapositive to prove that, for integers r and y: if a+y is odd, then exactly…

A: Here we use  Odd + Odd = Even Even +Even =Odd   Note:According to our guidelines we can solve only…