One of the following statements is property of continuous function f:X → Y: a) If C is Closed set in Y, then f-1(C)is closed set in X. b) If E is connected set in Y, then f1(E) is open set in X. c) If F is compact set in Y, then f¯(F) is compact set in х. d) If V is open set in X, then f(V) is open set in Y.

Q: Let X be a non-empty set. Define the function h : X → P(X), x → {x}. Which of the following is true?…

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Q: Let A, B, C be sets. Let f : A → B and g : B → C be functions. a) Prove that if f and g are…

A: We shall solve both parts of this question that you have posted.

Q: 15. Let A be an infinite set. Prove that there exists an injective function f: N→ A.

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Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: The solution of given problem is given as follows :

Q: Let f: X → Y and g : Y → Z be functions. (a) Show that if g of is one-to-one (or "injective"), then…

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Q: 3) Let X be a set with > 3 elements. Show that there exist bijective functions f :X → X and g : X +…

A: Let x=1,2,3 then, f=123132g=123321 `

Q: Use two of the following sets for each part below. Let X = {a,b,c}, Y = {1, 2, 3, 4} and Z = {s, t,…

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Q: Let f be a function from X to Y . For A ⊆ X, let also f(A) denote the set f(A) = {f(a) | a ∈ A}.…

A: This question is from sets.

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A: We have taken two different ordered pair of subsets of X and shown that their image is same. Hence f…

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Q: --to-one o? [ Se

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Q: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z?…

A: Let f be the subset of Z × Z defined by  f = {(ab, a + b) : a, b ∈ Z}. We observe that  That is the…