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…

A: Solution is given below

Q: Decide, among the following sets, which sets are subsets of one and another:A = { x : x ∈ R and x…

A: A = { x : x ∈ R and x satisfy x2– 8x + 12 = 0 } ={ x : x ∈ R and x satisfy (x-6)(x-2)= 0 }= {2,6} B…

Q: Let A and B be sets. Prove that A U B = A^ B if and only if A = B.

A:

Q: Let A and B be finite sets with A - B = {a, b, c, d, e, f, g} and An B = {h, i, j, k, l, m}. Find…

A:

Q: List the set in roster form. C=​{z​| z is an odd integer greater than 21 and less than or equal to…

A:

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

A:

Q: Complete the proof using only set identities and definitions. Suppose A, B, and C are any sets. Then…

A:

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if*

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: Let A, B and C are be sets. Show that we can have AnB= AnC without B=C

A:

Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

A:

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: Find an example of a set A with |A| = 3 which contains only other sets and has the following…

A:

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A: a)If sup A and sup B exists then          supA∪B=max{sup A,sup B} So supA∪B exists. First option is…

Q: Let X = {a,b,c,d}. List the elements of the set {A :A € P(X) and |A| = 2}.

A:

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

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

Q: List down the elements of the following sets {x ∈ ℝ : x2 + 5x = -6}

A: Explanation of the answer is as follows

Q: Let X be a set. Show that P(X)÷ X.

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

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

A:

Q: (FNB) UC'

A:

Q: Consider a set A with 10 elements.  How many different functions are there from the set A to a set…

A: Introduction: In mathematics, a function is an expression, rule, or law that specifies a…

Q: Let A, B and C be any three sets. Then Ax (BUC)=

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: Consider two sets A and B such that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the set C…

A:

Q: Prove the statement below.

A: Given, A and B be any sets. To prove that (A∩B)⊆(A∪B).

Q: Let U = {1, 2, 3, 4, 5} be the universal set. Let A = {1, 2, 3}, B = {1, 3, 5}, and C = {2, 4, 5}.…

A:

Q: Express the set in roster form. B= {x| xEN and x is even) Choose the correct answer below. O A. B=…

A: Please refer the attached image for complete solution.