Ah, what a lovely question! A subset is a set that contains only some elements of another set, while an equal set has the exact same elements as another set. It's like painting a beautiful landscape with different colors - each set has its own unique beauty, whether it's a smaller subset or an equal set. Just remember, every set is special in its own way!
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Equal sets are the sets that are exactly the same, element for element.
A proper subset has some, but not all, of the same elements. An improper subset is an equal set.
There is no difference between improper subset and equal sets. If A is an improper subset of B then A = B. For this reason, the term "improper subset" is rarely used.
Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.
A set "A" is said to be a subset of of set "B", if every element in set "A" is also an element of set "B". If "A" is a subset of "B" and the sets are not equal, "A" is said to be a proper subset of "B". For example: the set of natural numbers is a subset of itself. The set of square numbers is a subset (and also a proper subset) of the set of natural numbers.
A relation between two sets is defined to be any subset of the two set's Cartesian product. See related links for more information and an example.
The first part of the problem we take an object and break it down to four equal subset. Mathematical written as 1/4. The next step is to further divide each of the four subsets into four sub-subsets. That will give a total of sixteen sub sets of the whole. 1/4*1/4=1/16 or object divided into subset, subset, subset, subset and then each subset divided into sub-subset, sub-subset, sub-subset, sub-subset. Gives a total of sixteen sub-subset