Prove: f € R(a) if and only if for each ɛ > 0, there exists a partition of [a, b ] , say go, such that U(9,f,a) – L(»,f,a)< ɛ

Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs, t E S, sRt e…

A: Let A be any and let R be any binary relation on the set A. Relation R is symmetric if for a, b∈R,…

Q: Given: f = {(a,b),(b,a),(c,b)} a function from X = (a,b,c) to X a). Write f ∘ f as a set of…

A:

Q: Consider the set V = {(x, y) = R² : x+y=1}. on this set defined in the following way: (x2, y2) = (x₁…

A:

Q: Prove that Z3 x Zz is isomorphic to Zg.

A:

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is 9 an…

A: Let (M,d) be a metric space and let S⊆M. A point a∈S is said to be an Interior Point of S if there…

Q: Let f R2 R² be an isomorphism where : → ƒ ( [¹³]) = [()] and ƒ ([×4]) = }}] Find(G)

A:

Q: Let ƒ: R² → R² be an isomorphism where ([-])-[²] and f([:]) = [] = Find f ¹ƒ( [7¹]) X 0 2 2 0

A:

Q: A function, F: R × R ---› R x R has been defined as follows: F(x, y) = (3y - 1, 1 - x) for all (x,…

A:

Q: PROVE THE STATEMENT "There exists a, b ∈ Z+, such that if a > 1 and b > 1, then gcd(a, b) > gcd(a^3,…

A: Given statement is wrong because there is no a, b ∈ Z+, such that if a &gt; 1 and b &gt; 1, then…

Q: = Prove the operation of addition on the set Q = {[(x, y)] : x ≤ Z, y ≤ N} defined by [(x, y)] +…

A: Let us show that given operation is well defined.

Q: Prove that if f is a constant function on [a, b] then f = S(f,P) for any tagged partition P of [a,…

A: This is a question of R integration.

Q: Let G = Z, O Z, H = {(0, 0), (2, 0), (0, 2), (2, 2)}, and K = ((1, 2)). Is GIH isomorphic to Z, or…

A:

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

A: