Question

Please explain the closure property in the following set:
1.)The set of even numbers is closed under addition.
2.) {-1,0,1} is closed under addition and multiplication.

Answer 1

1. 2 even #'s added together yield an even #
2. Any of the #'s in the given set added together or multiplied together yield a # in the set.

Answer 2

ok thank u. can u give me some examples for no.1 and no. 2?

Answer 3

*for #2, make that any two unique #'s

Answer 4

sure
#1) 2+4=6, 6+4=10, 1000 + 2 = 1002, etc
#2) 1+0 = 1, 1+-1=0, etc. and 1*1 = 1, 1*0 = 0, -1* 1=1, etc

Answer 5

thank you so much! =]

Answer 6

* for addition on the previous post, i.e. you can't add 1 and 1 or -1 and -1

Answer 7

on natural numbers? is that what u mean?

Answer 8

no. for the second set, under addition it must be a+b, the set is not closed given a+a (i.e. 1+1=2, which isn't in the set. If you must use distinct #'s)

Answer 9

oh ok thank u