Are the following sets closed? Explain why / why not?

Question

a) The set {1, 2, 3, 4, 5} under addition?

b) The set {-1, 0, 1} under addition?

c) The integers under addition?

d) The set of positive integers under subtraction?

e) The set of natural numbers under division?

Answer 1

a) yes
b) no: 1+1 is not an element of the set
what do you think of the others?

Answer 2

oops
a) no: any sum bigger than 5 is not in the set