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How many sets of six numbers can you make with seven numbers?
7 To make it a bit more intuitive, think of it like this: If you have a set of 7 elements, you can "turn it into" a set of 6 elements by removing one of the elements. So, in how many ways can you remove an element from the set of 7 elements, without making the same 6-element set more than once?
How many subsets are there you 1 2 3 4 5 6 7 8 9 10 11?
Note that an empty set is included for the set of 11 numbers. That is 1 subset. Since order doesn't matter for this type of situation, we count the following number of subsets. 1-item subset: 11 choose 1 2-item subset: 11 choose 2 3-item subset: 11 choose 3 4-item subset: 11 choose 4 5-item subset: 11 choose 5 6-item subset: 11 choose 6 7-item subset: 11 choose 7 8-item subset: 11 choose 8 9-item subset: 11 choose 9 10-item subset: 11 choose 10 11-item subset: 11 choose 11 Note that the pattern of these values follows the Fibonacci sequence. If we add all of these values and 1 altogether, then you should get 2048 subsets that belong to the given set {1,2,3,4,5,6,7,8,9,10,11}. Instead of working out with cases, you use this form, which is 2ⁿ such that n is the number of items in the set. If there is 11 items in the set, then there are 211 possible subsets!
Why can an empty set have an element and a subset?
By definition an empty set cannot have any elements, otherwise it would not be empty!Think of a set as a container (like a box). The members of the set are those things inside it; there can be lots of things in a box, or just one, or none - when there are no items in the box it is empty, hence a set with no members is the empty set.A subset is made by taking some of the items from the set (or box) and putting them into another: many, one or no items can be taken to make the subset. It is always possible to take no items from a set, thus the empty set is a subset of ALL sets.For example, consider the set of people drinking coffee with 6 members: there are 3 latte drinkers, 1 cappuccino drinker, 2 espressos drinkers; various subsets can be made, eg:* those drinking lattes (3 members);* those drinking cappuccinos (1 member); or* those drinking tea (no members: the empty set - tea is not coffee and the original set is those who drink coffee).
Different between crisp set and fuzzy set?
In short, for a crisp set (subset) elements of the set definitely do belong to the set, while in a fuzzy set (subset) elements of the set have a degree of membership in the set. To make things clearer:Suppose we have a reference set X={x_1, ...} and a subset Y={y_1, ...} of X. If Y represents a crisp subset of X, then for all x_n belonging to X, x_n either belongs or Y or does not belong to Y. We can write this by assigning a function C which takes each member of X to 1 iff it belongs to Y, and 0 iff it does not belong to Y. E. G. Suppose we have the set {1, 2, 3, 4, 5}. For the crisp subset {1, 2, 4} we could write this in terms of a function C which takes 1 to 1, 2 to 1, 3 to 0, 4 to 1, and 5 to 0, or we can write {(1, 1), (2, 1), (3, 0), (4, 1), (5, 1)}.For a fuzzy subset F of a reference set X the elements of F may belong to F to a degree in between 0 and 1 (as well as may belong to F to degree 0 or 1). We can write this by assigning a function M which takes each member of X to a number in the interval of real numbers from 0 to 1, [0, 1] to represent its degree of membership. Here "larger" numbers represent a greater degree of membership in the fuzzy subset F. For example, for the reference set {1, 2, 3, 4, 5} we could have a function M which takes 1 to .4, 2 to 1, 3 to .6, 4 to .2, and 5 to 0, or {(1, .4), (2, 1), (3, .6), (4, .2), (5, 0)}, with 3 having a greater degree of membership in F than 4 does, since .6>.2.
How many Subset are there in 1 2 3 4 5 6 7 8 9 10?
Set A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }nA = 10 (there are 10 entries in A)|P(A)| = 2n|P(A)| = 210 = 1024P(A) represents the power set of A. The line brackets "|...|" represent the carnality (the count of elements). The power set is just a set of every possible set, including the empty set. I included this terminology to help research the topic further, if you are interested.The answer is 1024.Minor error in above answer: The term for the number of items in a set is its cardinality (not carnality).
