Show if A, B, C are connected subsets of X and A∩B not equal ∅ and...

Show if A, B, C are connected subsets of X and A∩B not equal ∅ and B ∩C not equal ∅, then A∪B ∪C is connected.

Expert Solution

Colby Messinger answered 2 years ago

Suppose A and B are closed subsets of R. Show that A ∩ B and A...

Suppose A and B are closed subsets of R. Show that A ∩ B and A ∪ B are closed.

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the...

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the subspace topology given by τs. 2. Let f: X → Y continue. We say that f is open if it sends open of X in open of Y. Show that the canonical projection ρi: X1 × X2 → Xi (x1, x2) −→ xi It is continuous and open, for i = 1, 2, where (X1, τ1) and (X2, τ2) are two topological spaces and...

Prove the following stronger variant of Proposition 7.4. Suppose C is collection of connected subsets of...

Prove the following stronger variant of Proposition 7.4. Suppose C is collection of connected subsets of a metric space X and B ∈ C. Show, if for each A ∈ C, A ∩ B not equal ∅, then Γ = ∪{C : C ∈ C} is connected. [Suggestion: Consider the collection D = {C ∪ B : C ∈ C}].

Let A , B , and C be disjoint subsets of the sample space. For each...

Let A , B , and C be disjoint subsets of the sample space. For each one of the following statements, determine whether it is true or false. Note: "False" means "not guaranteed to be true." a) P(A)+P(Ac)+P(B)=P(A∪Ac∪B) b) P(A)+P(B)≤1 c) P(Ac)+P(B)≤1 d) P(A∪B∪C)≥P(A∪B) e) P((A∩B)∪(C∩Ac))≤P(A∪B∪C)P((A∩B)∪(C∩Ac))≤P(A∪B∪C) f) P(A∪B∪C)=P(A∩Cc)+P(C)+P(B∩Ac∩Cc) ) Please explain how you got the answer.

(Connected Spaces) (a) Let <X, d> be a metric space and E ⊆ X. Show that...

(Connected Spaces) (a) Let <X, d> be a metric space and E ⊆ X. Show that E is connected iff for all p, q ∈ E, there is a connected A ⊆ E with p, q ∈ E. b) Prove that every line segment between two points in R^k is connected, that is Ep,q = {tp + (1 − t)q | t ∈ [0, 1]} for any p not equal to q in R^k. C). Prove that every convex subset...

If I show (A and (B → C)) → D and (A and (C → B))...

If I show (A and (B → C)) → D and (A and (C → B)) → D, can I conclude A → D?

What is C if X = (A + B – C) / C and X =...

What is C if X = (A + B – C) / C and X = 0.1454, A = 204, and B = 11,214? Round answer to nearest whole number. What is D if D = A – B – C and A = 0, B = -8,673, and C = 4,186? Round answer to nearest whole number. What is M if R = F + ((B × (M – F))) and R = 0.2353, B = 1.8, and F...

1. Show that when two equal resistances are connected in parallel the equivalent resistance is just...

1. Show that when two equal resistances are connected in parallel the equivalent resistance is just one half that of either resistor. 2. Suppose that we replaced one of the bulbs in the setup with one rated at 6V, 7.5W. show that a 1A fuse in the circuit would blow out when this bulb is given power. What is the operating resistance of the filament in this bulb? Show Calculation

For the following exercises, find the number of subsets in each given set. {a, b, c, … , z}

For the following exercises, find the number of subsets in each given set.{a, b, c, … , z}

Suppose A and B are subsets of R, and deﬁne: d(A,B) = inf{|a−b| : a ∈...

Suppose A and B are subsets of R, and deﬁne: d(A,B) = inf{|a−b| : a ∈ A,b ∈ B}. (a) Show that if A∩B 6= ∅, then d(A,B) = 0. (b) If A is compact, B is closed, and A∩B = ∅, show d(A,B) > 0. (c) Find 2 closed, disjoint subsets of R (say A and B) with d(A,B) = 0

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