Question

If for integers a, b we define a ∗ b = ab + 1, then: (a)...

If for integers a, b we define

a ∗ b = ab + 1,

then:

(a) The operation ∗ is commutative ?

(b) The operation ∗ is associative ?

Modern Algebra

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If for integers a, b we define a ∗ b = ab + 1, then: (a)...
If for integers a, b we define a ∗ b = ab + 1, then: (a) The operation ∗ is commutative ? (b) The operation ∗ is associative ? Modern Abstract Algebra, please explain, thanx
Define a+b=a+b -1 and a*b=ab-(a+b)+2 Assume that (Z, +,*) is a ring. (a) Prove that the...
Define a+b=a+b -1 and a*b=ab-(a+b)+2 Assume that (Z, +,*) is a ring. (a) Prove that the additative identity is 1? (b) what is the multipicative identity? (Make sure you proe that your claim is true). (c) Prove that the ring is commutative. (d) Prove that the ring is an integral domain. (Abstrat Algebra)
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b)...
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b) If a and b are positive integers, then show that lcm(a, b) is a multiple of gcd(a, b).
determine conditions on integers a and b for which ab is even. then prove that the...
determine conditions on integers a and b for which ab is even. then prove that the conditions are true.
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a,...
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) = 1. (Hint: use the GCD characterization theorem.) (b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (Hint: you can use the GCD characterization theorem again but you may need to multiply equations.) (c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if and...
Recall from class that we defined the set of integers by defining the equivalence relation ∼...
Recall from class that we defined the set of integers by defining the equivalence relation ∼ on N × N by (a, b) ∼ (c, d) =⇒ a + d = c + b, and then took the integers to be equivalence classes for this relation, i.e. Z = [(a, b)]∼ | (a, b) ∈ N × N . We then proceeded to define 0Z = [(0, 0)]∼, 1Z = [(1, 0)]∼, − [(a, b)]∼ = [(b, a)]∼, [(a, b)]∼...
Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that...
Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that do not use the prime factorizations of a and b.
Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a...
Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a − b). Justify your answer. (abstract algebra)
let g be a group. let h be a subgroup of g. define a~b. if ab^-1...
let g be a group. let h be a subgroup of g. define a~b. if ab^-1 is in h. prove ~ is an equivalence relation on g
(a) Let A ⊂ R be open and B ⊂ R. Define AB = {xy ∈...
(a) Let A ⊂ R be open and B ⊂ R. Define AB = {xy ∈ R : x ∈ A and y ∈ B}. Is AB necessarily open? Why? (b) Let S = {x ∈ R : x is irrational}. Is S closed? Why? Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT