SOLUTION: Is {0,2,4,6} closed under multiplication? Or Is {1,3,5,7} closed under multiplication? Please help!

Question 1002316: Is {0,2,4,6} closed under multiplication? Or Is {1,3,5,7} closed under multiplication?
Please help!
Found 2 solutions by addingup, Theo:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
multiplying odd numbers always produces odd numbers, so odd numbers are closed under multiplication
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the statement is a little bit confusing.

the definition of closure is that the operation on the set yields a member of the same set.

based on that definition, the set {0,2,4,6} is not closed under multiplication because 2*4 = 8 and 2*6 = 12 and 4*6 = 24 are not members of that set.

similarly, the set of {1,3,5,7} is not closed under multiplication because 3*5 = 15 and 3 * 7 = 21 and 5 * 7 = 35 are not members of that set.

now, if you define {0,2,4,6} as being members of the set of even numbers, then it is closed under multiplication because the results of multiplying an even number by an even number will always yield an even number.

same with {1,3,5,7} being defined as members of the set of odd numbers. it is then closed under multiplication because any odd number multiplied by any odd number will will always yield an odd number.

so, if your sets are defined as being ONLY those elements shown, neither set is closed under multiplication.

here's some references that may help you.

http://mathbitsnotebook.com/Algebra1/RealNumbers/RNClosure.html

http://www.regentsprep.org/regents/math/algebra/an1/closure.htm

https://answers.yahoo.com/question/index?qid=20090901203653AALmEAw

http://www.cwladis.com/math100/Lecture2Groups.htm

since your problem didn't defined what the sets are closed under (like set of integers or set of even numbers, etc), then you are dealing with only members of those sets shown and therefore both are not closed under multiplication or additon for that matter.

that's my take.

RELATED QUESTIONS
is (1, 1/2, 1/3, 1/4, 1/5, ...) closed under multiplication? (answered by DrBeeee)
Is the set {-1,0,1} closed under... (answered by KMST)
Determine if the following sets are closed under multiplication: a. {0} b. {1, 3, 5, 7, (answered by stanbon)
1.)Is the interval [0,1] closed under multiplication. ? Is yes, why? If no, give... (answered by richard1234)
The set of positive real numbers is closed under which operation(s)? is it... (answered by rapaljer)
A set is said to be closed under multiplication if the product of elements in the set... (answered by Fombitz)
Under which operations is the set of whole numbers {0, 1, 2, 3, �} closed? A.... (answered by Fombitz)
Which of the following sets of numbers is closed under multiplication? {-2,-1,0,1}... (answered by stanbon)
Is the following true or false? The set of whole numbers is closed under subtraction... (answered by askmemath)