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How many patterns of subset can you make from a set?
given any set of n objects, there are 2^n subsets. This comes from the fact that each item is either in or not in any given subset. So for all n objects, each one has two possibilities, either it is or is not in a subset. Then 2^n come from the multiplication principle.
Can two points determine a plane?
No, 2 points define a line, 3 points define a plane.
What are example of proper subset?
{1,2,4.7} is a proper subset of {1, 2, 3, 4, 4.7, 5}
Why does a set containing n element have 2n subsets?
I presume you meant 2^n (2 raised to the nth power), not 2*n (2 times n). That's answers.com's character set problem again (I trust, giving you the benefit of the doubt). The answer is that for each of the n elements, it is either in any particular subset or it isn't. Which elements are in and which are not in a subset defines the subset. So for example, if n is 3, say a, b, and c, there are 2 sub-collections of the set of all subsets: those containing a and those not containing a. In each of those sub-collections, there are 2 sub-collections based on whether they contain b, for a total of 4 (2*2) sub-collections. Finally, of each of these 4, there are 2 subsets: those containing c and those not containing c, for a total of 8 (2*2*2 or 2^3) subsets. Got it?
What is trivial subset?
The trivial subsets of a set are those subsets which can be found without knowing the contents of the set. The empty set has one trivial subset: the empty set. Every nonempty set S has two distinct trivial subsets: S and the empty set. Explanation: This is due to the following two facts which follow from the definition of subset: Fact 1: Every set is a subset of itself. Fact 2: The empty set is subset of every set. The definition of subset says that if every element of A is also a member of B then A is a subset of B. If A is the empty set then every element of A (all 0 of them) are members of B trivially. If A = B then A is a subset of B because each element of A is a member of A trivially.
