Closure is defined as a given operation staying within a set (i.e. an operation such as subtraction on two numbers which are in the set of natural numbers will result in a number in the natural numbers)
For natural numbers:
They are not closed under subtraction. 1 - 2 = -1 (both 1 and 2 are natural numbers but -1 is not)
They are closed under multiplication. 3 * 2 = 6 (3, 2, and 6 are natural numbers)
They are not closed under division.
(1 and 2 are natural numbers, but 1/2 is not a natural number).
For integers:
They are closed under addition. 1 + 1 = 2 (both 1 and 2 are natural numbers)
They are closed under subtraction. 2 - 4 = -2 (2, 4, and -2 are integers)
They are closed under multiplication. 1 * 0 = 0 (1 and 0 are integers)
They are not closed under division.
(1 and 2 are integers, but 1/2 is not an integer)