4. Let C₁ be the set of all continuous real-valued functions on I = [0, 1]. (a) Show that d : C₂ × C'₁ → R defined by d(ƒ, g) = [¹ \ƒ(x) — g(x)| da is a metric on C₁. (b) Define i [0, 1] → R by i(x): = x. Give three examples of elements of Ba(i, 1).

Q: 6. Let A be a set. Prove there exists a unique subset B of A such that if C is of A, then BnC=C. any…

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A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

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Q: Let X be a set. Show that P(X)÷ X.

A: Solution:Let X ba a set.To Prove: P(X)≠X

Q: (FNB) UC'

A:

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A: Take x in left hand side and prove it belong to A and vice versa.

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Q: Let denote the empty set. The power set of the set {0} is: Select one: O a. {0} O b. {0, {0}} O c.…

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