Final answer:
Set A = {0,1,2,3,4,5,...} is closed under multiplication since any product of two elements remains in the set. However, set A is not closed under subtraction as subtracting a larger element from a smaller one results in a negative number, which is not in the set. Therefore, the correct answer is (c).
Step-by-step explanation:
The set A = {0,1,2,3,4,5,...} represents the set of all non-negative integers, also known as natural numbers including zero. When we talk about a set being 'closed' under an operation, we mean that performing that operation on any two elements of the set will result in another element that is also within the set.
Closed under multiplication: When we multiply any two elements of set A (e.g., 2x3=6 or 4x0=0), we always get another non-negative integer, which means A is closed under multiplication.
Not closed under subtraction: However, if we subtract a larger number from a smaller one (e.g., 2-3=-1), we get an integer that is not in set A, which means A is not closed under subtraction.
The correct answer is (c) Not closed under subtraction, closed under multiplication.