if by Numbers you mean Integers, then the answer is TRUE. if it is real numbers, then it is false.
No. One of the group axioms is that each element must have an inverse element. This is not the case with integers. In other words, you can't solve an equation like: 5 times "n" = 1 in the set of integers.
False.
The set of positive integers contains 1 but not zero. Within the set of integers, there is the subset of positive integers, the subset of negative integers and the subset with a single element in it - zero. There are a zillion other sets that could be specified that meet the conditions set down in the question. The one cited is an easy one.
true
if by Numbers you mean Integers, then the answer is TRUE. if it is real numbers, then it is false.
That is not true.
That's false.
False. The collection of natural numbers is an example of a set, not an element. An element is an individual member of a set, while the collection of natural numbers is a set itself.
No.
True. Zero is in the set of whole numbers, integers, rational numbers and real numbers but not natural numbers. Natural numbers are often referred to as the "counting numbers" or how you learned to count. When we are teaching little children numbers, we never start with zero or negative numbers - just 1, 2, 3...
It isn't. The empty set is not a proper subset of the empty set.The empty set is a subset of every set, for the following reason. "A" is a subset of "B" means that if an item "x" is an element of "A", then it is also an element of "B".(x is element of A) implies (x is element of B)Since the empty set has no elements, the left part of the implication is false. Therefore, the entire implication is true. If you have trouble grasping this last part, look up the Wikipedia article, or other sources, for "trivially true" or "vacuous truth". (Briefly, an implication, like "F implies G", can only be false if "F" is true, and "G" is false - in all other cases, it is true.)
No. One of the group axioms is that each element must have an inverse element. This is not the case with integers. In other words, you can't solve an equation like: 5 times "n" = 1 in the set of integers.
True.
False.
false, because the complement of a set is the set of all elements that are not in the set.
A set of which all the elements are contained in another set. The set of even numbers is a subset of the set of integers.