Properties of Operations, math homework help
1. Determine which of the operations on the positive integers are: commutative; associative; idempotent; which have identities; and of those, which have inverses for all elements.
(a) addition
(b) multiplication
(c) M defined by aM b = larger ofa andb
(d) m defined by amb = smaller of a and b
(e) @ defined by a@b = a^b
2. Prove that intersection of closed subsets is closed.