The empty element is a subset of any set--the empty set is even a subset of itself. But it is not an element of every set; in particular, the empty set cannot be an element of itself because the empty set has no elements.
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A set "A" is said to be a subset of "B" if all elements of set "A" are also elements of set "B".Set "A" is said to be a proper subset of set "B" if: * A is a subset of B, and * A is not identical to B In other words, set "B" would have at least one element that is not an element of set "A". Examples: {1, 2} is a subset of {1, 2}. It is not a proper subset. {1, 3} is a subset of {1, 2, 3}. It is also a proper subset.
An element x, of a set S has an additive inverse if there exists an element y, also in S, such that x + y = y + x = 0, the additive identity.
The mode is the data set element(s) that is(are) repeated the most. If every data set element occurs the same number of times, there is no mode. As there is only one occurrence of each data set element in {11, 12, 13} there is no mode. If your data set read {11, 12, 12, 13, 13, 12} your mode would be 12. If your data set read {11, 12, 12, 13, 13} your modes would be 12 & 13.
It is called the "soulltion set"
The closure property is an attribute of a set with respect to a binary operation, not only a binary operation. A set S is closed with respect to multiplication if, for any two elements, x and y, belonging to S, x*y also belongs to S.