Let R=R+. Define: a+b = ab ; ab = a^(lnb) 1. Is (R+, +, ) a...

Let R=R+. Define:

a+b = ab ; a*b = a^(lnb)

1. Is (R+, +, *) a ring?

2. If so is it commutative?

3. Does it have an identity?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Define the greatest lower bound for a set A ⊂ R. Let A and B be...

Define the greatest lower bound for a set A ⊂ R. Let A and B be two non-empty subsets of R which are bounded below. Show glb(A ∪ B) = min{glb(A), glb(B)}.

1. Let a < b. (a) Show that R[a, b] is uncountable

Define a sequence from R as follows. Fix r > 1. Let a1 = 1 and...

Define a sequence from R as follows. Fix r > 1. Let a1 = 1 and define recursively, an+1 = (1/r) (an + r + 1). Show, by induction, that (an) is increasing and bounded above by (r+1)/(r−1) . Does the sequence converge?

Let A and B be two non empty bounded subsets of R: 1) Let A +B...

Let A and B be two non empty bounded subsets of R: 1) Let A +B = { x+y/ x ∈ A and y ∈ B} show that sup(A+B)= sup A + sup B 2) For c ≥ 0, let cA= { cx /x ∈ A} show that sup cA = c sup A hint:( show c supA is a U.B for cA and show if l < csupA then l is not U.B)

in the group R* find elements a and b such that |a|=inf, |b|=inf and |ab|=2

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by...

Let S = {1,2,3,4} and let A = SxS Define a relation R on A by (a,b)R(c,d) iff ad = bc Write out each equivalence class (by "write out" I mean tell me explicitly which elements of A are in each equivalence class) Hint: |A| = 16 and there are 11 equivalence classes, so there are several equivalence classes that consist of a single element of A.

For each pair a, b with a ∈ R − {0} and b ∈ R, define...

For each pair a, b with a ∈ R − {0} and b ∈ R, define a function fa,b : R → R by fa,b(x) = ax + b for each x ∈ R. (a) Prove that for each a ∈ R − {0} and each b ∈ R, the function fa,b is a bijection. (b) Let F = {fa,b | a ∈ R − {0}, b ∈ R}. Prove that the set F with the operation of composition of...

(V) Let A ⊆ R, B ⊆ R, A 6= ∅, B 6= ∅ be two...

(V) Let A ⊆ R, B ⊆ R, A 6= ∅, B 6= ∅ be two bounded subset of R. Define a set A − B := {a − b : a ∈ A and b ∈ B}. Show that sup(A − B) = sup A − inf B and inf(A − B) = inf A − sup B

Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be...

Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be the relation define on A where (a, b)R(c, d) means that 2 a + d = b + 2 c. a. Prove that R is an equivalence relation. b. Find the equivalence classes [(−1, 1)] and [(−4, −2)].

Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if...

Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if and only if ad=bc. (a) Show that R is an equivalence relation. (b) What is the equivalence class of (1,2)? List out at least five elements of the equivalence class. (c) Give an interpretation of the equivalence classes for R. [Here, an interpretation is a description of the equivalence classes that is more meaningful than a mere repetition of the definition of R. Hint:...

Subjects

Question

Let R=R+. Define: a+b = ab ; a*b = a^(lnb) 1. Is (R+, +, *) a...

Solutions

Expert Solution

Related Solutions

Let R=R+. Define: a+b = ab ; ab = a^(lnb) 1. Is (R+, +, ) a...