Question

Let n=60, not a product of distinct prime numbers. Let B_n= the set of all positive...

Let n=60, not a product of distinct prime numbers. Let B_n= the set of all positive divisors of n. Define addition and multiplication to be lcm and gcd as well. Now show that B_n cannot consist of a Boolean algebra under those two operators.

Hint: Find the 0 and 1 elements first. Now find an element of B_n whose complement cannot be found to satisfy both equalities, no matter how we define the complement operator.

Math   Algebra   
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
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. For this relation R: Show that the equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq. you may use the following lemma: If p is prime...
Let p and q be any two distinct prime numbers and define the relation a R...
Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. I need to prove that: a) R is an equivalence relation. (which I have) b) The equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq I...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT