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

Q: If  X is a countable set show that every topology on X is second countable.

A: To Show: If  X is a countable set show that every topology on X is second countable.

Q: State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram…

A: The formula for The principle of inclusion and exclusion  for three sets A |A\cup B \cup C| = |A| +…

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

A:

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

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set.

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: Let B be a set and {A: aeA} be an arbitrary family of sets. Then BUn A) = %3D

A: Answer

Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let 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: Show

A: We prove this statement by using definition of Borel Set.

Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

A:

Q: The set of elements common to both set A and set B is called the of sets A and B, and is symbolized…

A: The set of elements common to both set A and set B is called the ________ of sets A and B, and is…

Q: Show that every open set with respect to 7 is a union of open ball(s).

A:

Q: The set of elements that are members of set A or set B or of both sets is called the. of sets A and…

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

Q: Prove that for any sets A, B, C, ANB = AN C and AUB= AUC if and only if B = C. %3D Prove that for…

A:

Q: Choose any that is a subset of the set (Ø} {{Ø),0} {{1}}

A:

Q: A set which has ho element is said to be

A: A set with no elements = { }

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: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

A:

Q: Use the method of intersection of sets to compute the following. (a) GCD(12,16,8) and LCM(12,16,8)…

A:

Q: Suppose A, B, C are sets. what do you need to show to prove the fllwing definition of subset:…

A: If x is a general element in P ,the given statement implies that each element in P is also in Q…

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: @ (А-В)- С 3 (А - С) - В

A: Introduction :

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

A:

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

A:

Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: Use the element method for proving a set equals the empty set to prove that: For any A, B sets, (An…

A: Since you have post multiple question I only solve first one.

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

A: Set equality

Q: Prove that for all sets A, B, and C, if CCB-A, then AnC=0.

A:

Q: Let {S,}EN is a disjoint seqeuence of measurable sets , then: US, µ(S,)

A: Given a statement

Q: Let {S,},EN is a disjoint seqeuence of measurable sets , then: HUS,

A:

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

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

A:

Q: The closare of a set is smallest closed set containing s صواب ihi

A: Let S be a subset of X: S⊆X. Let M be the closure of S. Then M is the smallest closed set which…

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: 7. Show that the Obenchain class LOb(B) is a convex set.

A: Given: To show the Obenchain class LOb (β) is a convex set is given as,

Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

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

A:

Q: let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are…

A: Given that X=a,b,c. To construct two topologies that have at least four open sets. We know that in…

Q: prove that the union of a countable set and an uncountable set is uncountable

A:

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: open ball is the open set

A:

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

A:

Q: An indexed family of sets (A,hcs is said to be a cover of a set X if and only if X CU,crA Use this…

A: Let A be a non-empty set and Cii∈I and Djj∈J are two different covers of A. Since Cii∈I is cover of…

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

A:

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

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.