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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).
What subset is?
For example, if we have a set of numbers called A which has 3 members(in our case numbers): A={2,5,6} this set has 8 subsets (2^3) which are as follow: the empty set: ∅ {2},{5},{6} {2,5},{2,6},{5,6} {2,5,6}
How many subsets does 6 elements have?
If you have a set of 6 elements, you can make a total of 26 different subsets - including the empty set and the set itself.
How many elements are in the set ABC 1 3 6?
There are four elements: ABC, 1, 3 and 6.
Is a subset smaller or larger then a regular set?
A subset is smaller. A subset is made up of entries from the regular set, so it cannot be bigger, and it cannot be the same size, because that would just be the regular set again. Example: {2, 3, 5} is a subset of {2, 3, 4, 5, 6}
How many subsets can be made from a set with 6 elements?
If a set has six elements, for example {A, B, C, D, E, F}, then it may have the following subsets: - the set itself - 6 sets of five elements - 15 sets of four elements - 20 sets of three elements - 15 sets of two elements - 6 sets of one element - 1 set with no elements (the null set), for a total of 64 sets, which is 2^6, or 2 to the 6th power.
How many elements are there if a set has 63 proper subsets?
6
How many two elements subsets does a 4 element set have?
6
Why is 6 a sub set of 2?
6 is a subset of 2 because 6 is a even number and 2 can divide 6 evenly
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.
