Let Fa be a closed set for each a e T. Show that Fa is closed. (Show that an arbitrary intersection of closed sets is a closed set.)

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Q: 2. Let f be defined on an open interval (a, b) and assume that for some e e (a, b) we have f'(c) > 0…

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Q: Suppose R and S are symmetric relations on a set A. Prove that RoS is symmetric iff RoS = So R.

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A: Let T be a topological construct onℝ defined by the formT={ϕ,ℝ}∪Ea=(a,∞);a∈ℝ

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A: If there exists an one-one map from D to C then "|D| < |C|" or "|C| >|D|".

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Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x € R: 1/x e A}. 1…

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Q: Let T and M be a non-empty families of sets with T  ⊆ M. Show that ∩T  ⊆ ∪ M.

A: Given: T and M are families of sets with T⊆M. To show: ∩T ⊆∪M

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Q: C.1 Let r > 0 and define the closed ball by B,(x) = {y € X : d(x,y) <r} Show that B(x) is closed set…

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Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

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Q: Let A and B be sets. Fill in the blanks to define precisely what it means for A to be a subset of B.…

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Q: Let V C(R ) be a nonempty open set satisfying a – b EV whenever a, b e V. Prove that V = R. %D

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Q: Let S and T be finite sets, and let f: S T be a map. Then |S| = IS {}| YET Select one: O True OFalse

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Q: Let A = {x ER|a° e Q} be a set. Is A countable? Justify the answer by showing the explicit formula…

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Q: Let A={(m,n)∣m,n∈N and gcd(m,n)=1} and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc…

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Q: Let k e Zt. Let A be a set such that |A| = k + 1, and let a e A (i.e., a is a fixed but unspecified…

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Q: 3. Let a, b e R such that a < b. Prove that the open interval (a, b) is an open set in R.

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Q: Let X, Y be two sets. Prove that X x YC P(P(X UY )).

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Q: Let k e Zt. Let A be a set such that |A| = k + 1, and let a e A (i.e., a is a fixed but unspecified…

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Q: For nonempty sets A, B, and C, let f: A -> B and g: B-> C. If g is onto, then gof is onto.

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Q: An operation * on a set S is a relationship that assigns to some ordered pair of elements of S a…

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Q: Show that if E is any measurable set, then -v (E) < v(E) < v*(E) and |v( E)| < \v|(E).

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