Is the number of sets a subset of the set?

Your title is wrong. After careful observation, I am sure that it is not an intersection, it must be a union, and the title should be like this:

a,a1,a2...am} and b=, then the possible types of set b are as many as 2 to the m power.

It does not refer to a subset.

The reason is that b must contain every one of them, and the fact that the package does not contain each of them does not affect the validity of that equation.

So each package does not contain 2 cases, and the total number of cases is 2 to the m power. So it is possible that the combination of b has 2 to the m power.

It is the number of sets b that make the intersection b = true.

The number of sets is not the number of subsets, because a set can have many subsets. You will not be able to answer the questions you have added.

You can memorize formulas.

If there are n elements of a set, then its subset has 2 to the nth power (note the existence of empty sets), .A non-empty subset has 2 to the nth power minus 1, a true subset has 2 to the nth power minus 1, and a non-empty true subset has 2 to the nth power minus 2.

If there are few elements, you can use the enumeration method.

However, the best way to do this is to use the binomial theorem.

For example. Know that there are n elements in a set (c below represents the combination, where ncr represents the selection of r elements from the n elements to combine).

First of all, there are 0 elements in the subset and there is [nc0].

There is [nc1] if there is 1 subset element

There are 2 subset elements with [nc2].

There are m subset elements with [ncm].

Those with n-1 subset elements have [nc(n-1)].

There are n subset elements with [ncn].

So there is [nc0]+[nc1]+[nc2]+.... in a finite setncm]+…nc（n-1）]+ncn]

According to the binomial theorem.

Know[nc0]+[nc1]+[nc2]+....ncm]+…nc（n-1）]+ncn]=2^n

If there are n elements in a set, the number of subsets of the set is 2 nTrue subsetThe number of is (2 n)-1.

A subset is a mathematical concept: if any one of the elements of set A is an element of set B, then set A is called a subset of set B. Symbolic language: if a a, both a b, then a b.

Nature of the subset:1. According to the definition of subset, we know a a. That is, any one set is a subset of itself.

Second, for empty sets, we stipulate a, i.e., empty sets are a subset of any set.

Note: If a= then a is still true.

To any set of s,powers of s.

Ordering by inclusion is a bounded lattice, which, in combination with the above proposition, is a Boolean algebra.

A total of 2 subsets to the nth power. If any element of set A is an element of set B (any a a then a b), then set A is called a subset of set B, denoted as a b or b a, and is read as "set A contains set B" or set B contains Set A".

i.e.: a a has a b, then a b.

Quality. 1. According to the definition of subset, we know a a. That is, any one set is a subset of itself.

Second, for empty sets, we stipulate a, i.e., empty sets are a subset of any set.

Note: If a= then a is still true.

Proof: Given any set a, it is to be proved that is a subset of a. This requires that all elements given are elements of a; However, there are no elements.

For experienced mathematicians, the corollary is that "there are no elements, so all elements are elements of a.""Yes, obviously; But for beginners, there are some troubles. Because there are no elements, how to make"these elements"Become an element of another collection? A different way of thinking would help.

All subsets: ,

1. An empty set is a subset of all sets;

2. The subset containing 1 element is: , ,

3. The subset containing 2 elements is: , ,

4. The subset containing 3 elements is:

Let s and t be two sets if all elements of s belong to t, ie.

then s is said to be a subset of t, denoted as.

The subset containing 1 element is ,,;

The subset containing 2 elements is ,,;

There are 8 subsets of 3 elements.

The subset contains 0, 1, 2, or 3 of the three elements, 1, 2, and 3, respectively.

Analysis According to the definition of a subset, all subsets of the set can be written in order of the number of elements in the subset

Answer: The subset of the set is , comment Examine the concept of the subset of the set, pay attention to distinguish between the numerator set and the true subset, and don't miss the empty set

All subsets and empty sets are subsets of all sets; 2. The subset containing 1 element and the subset containing 2 elements are:

The subset with 3 elements is: Let s and t be two sets, if all the elements of s belong to t, then s is said to be a subset of t, denoted as an extended data set of finite set a, the number of elements of set a is n1, and the number of subsets of a is an n-power of 2; 2. The number of true subsets of a is the nth power of 2 minus one; 3. The number of non-empty subsets of a is the nth power of 2 minus one; 4. The number of non-empty true subsets of a is to the nth power of 2 minus two; 5. An empty set is a subset of any set and a true subset of any non-empty set; 6. Any set is a subset of itself, i.e., a a; An empty set has only one subset, which is itself; 7. The subset and true subset of the set are transitive: if a b, b c, then a c; If a b, b c, then a c.

What is the number of subsets of the set a={1,2,3}?

What is the number of subsets of the set a={1,2,3}?

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User 4367570282485

The set a = (1,2,3,4) has a total of 26 subsets.

Solution: Since set a = has four elements, the elements of a subset of set a can be 0, 1, 2, 3, 4.

When the elements of a subset of set A are 0, the number of subsets is c(4,0)=1, when the elements of a subset of set A are 1, the number of subsets is c(4,1)=4, when the elements of a subset of set A are 2, the number of subsets is c(4,2)=6, when the elements of a subset of set A are 3, the number of subsets is c(4,3)=4, and when the elements of a subset of a set A are 4, the number of subsets is c(4,4)=1.

Then the total number of subsets of set a is 1+4+6+4+1=26.

Extended information: 1. Classification and nature of the set.

1) Empty set. An empty set is a true subset of any non-empty set. An empty set is a subset of any one collection.

2) Subset. Let s and t be two sets, and if all elements of s belong to t, then s is a subset of t.

2. The law of operation of sets.

For sets a, b, and c, they conform to the following laws of operation.

1) Commutative law.

a∩b=b∩a、a∪b=b∪a

2) Associative law.

a∪(b∪c)=(a∪b)∪c、a∩(b∩c)=(a∩b)∩c

3) The law of identity.

a∪=a；a∩u=a

For example, a set is a=

These are the five elements.

So the number of its subsets should be 2 to the fifth power, i.e. 32 so the number of subsets of the set containing n elements is the formula = 2 to the nth power.

A set contains n elements, and for any one of them, it is either in its subset or not there, and there is absolutely no other possibility. There are 2 possibilities. There are 2 kinds of each element, and the number of subsets obtained by the principle of multiplication is 2 n.

A set contains five elements and the number of its subsets.

A subset is a mathematical concept that has 2 n subsets for a set of n elements. which is empty set and itself.

In addition, the number of non-empty subsets is 2 n -1

The number of true subsets is 2 n -1;

The number of non-null true subsets is 2 n -2

Definition: If any element of set A is an element of set B (any a a then a b), then set A is called a subset of set B. For two non-empty sets A and B, if any one element of set A is an element of set B, we say A b (read as a contains b), or B a (read as b contains a), and says that Set A is a subset of Set B.

Sets are of incomparable special importance in the field of mathematics.

The foundation of set theory was laid by the German mathematician Cantor in the 70s of the 19th century, and after half a century of efforts by a large number of scientists, by the 20s of the 20th century, it has established its basic position in the system of modern mathematical theory.

Characteristic. 1. Mutual heterogeneity.

Any two elements in a set are considered to be different, i.e. each element can only appear once. Sometimes you need to characterize the situation where the same element appears more than once, you can use a multiset where the element is allowed to appear more than once.

2. Certainty.

Given a set, any element that either belongs to the set or does not belong to the set must be one or the other, and no ambiguity is allowed.

If there are n elements in a set (which can be numbers), then the number of all its subsets is 2 n, the number of all true subsets is 2 n-1 (subset minus itself), the number of all non-empty subsets is 2 n-1 (subset minus empty set), and the number of all non-empty true subsets is 2 n-2 (subset minus itself and empty set).

For example, all subsets of the set are: , a total of 2 4 = 16.

The above conclusions can be proved by the counting principle and the binomial orthogonal theorem.

Calculation process: know that there are n elements in a set (c below represents the combination, where ncr represents the selection of r elements from the n elements to combine).

First of all, there are 0 elements in the subset and there is [nc0].

There is [nc1] if there is 1 subset element

There are 2 subset elements with [nc2].

There are m subset elements with [ncm].

Those with n-1 subset elements have [nc(n-1)].

There are n subset elements with [ncn].

So there is [nc0]+[nc1]+[nc2]+.... in a finite setncm]+?nc（n-1）]+ncn]

According to the binomial theorem, [nc0]+[nc1]+[nc2]+?ncm]+?nc（n-1）]+ncn]=2^n