Math problems , and, or, and the difference

You put mathematical symbols.

Confused with logical language!

The mathematical symbols are u and , and u means union, which means intersection.

Set two sets A and B:

AUB is equal to the set of all the elements of set A and set B;

a b is equal to the set of the same elements in set a and set b.

And and is a conjunction, or a logical proposition.

and means a compound proposition composed of two or more propositions, as long as one of the propositions is false, then the compound proposition is false, all propositions are true, and the compound proposition is true; or a compound proposition consisting of two or more propositions, as long as any one of them is true, then the compound proposition is true, and all propositions are false, and this proposition is false.

Set the proposition"x"and propositions"y"：

1) Propositions"x and y"

If"x"is false,"y"true; "x"is false,"y"is false,"x"true; "y"For false, then proposition"x and y"is false,

If"x"with"y"At the same time true, then proposition"x and y"true;

2) Propositions"x or y"

If"x"is false,"y"true; "x"is false,"y"is false,"x"true; "y"If it is true, then it is a proposition"x or y"true;

If"x"with"y"At the same time false, then the proposition"x or y"is false,

So, you haven't figured it out yet"u","∩"，"or"and"And"relationship. Strictly speaking, the first two are operators.

The last two are logical relationship connectors.

Although mathematics and logic.

are two different disciplines, but the two disciplines are more closely related. So it's often found in mathematics as well"And"with"or"；It also comes up a lot in logic"u"with"∩"。Just figure out their own rules of operation.

While"with"It's just a connective, mathematically speaking, it doesn't carry any operational significance; From a logical point of view, he does not express any logical judgment relationship!

I hope it can be helpful to you, these things need to be understood in practical use, these four things are still relatively easy to understand!

1，2）u（3，4）

1,2) (3,4) = empty set.

1,2) and (3,4), this one does not make sense. For sum or connection should be two propositions, not two sets.

1,2) or (3,4), this also doesn't make sense, for the same reason as above.

1, 2) and (3, 4), this one does not make any sense.

Or: If one of these conditions is met.

And: all of them are satisfied.

In the union of sets, all the different elements in multiple sets must be found in it, that is, one element in multiple sets can be found in it.

The meaning is analyzed concretely.

u is the meaning of union, that is, to merge two sets, is the meaning of intersection, is to find the part of the two sets that coincide, is the meaning of belonging, that is, the elements on the left belong to the set on the right.

Union Definition: A set of all elements belonging to set A or belonging to set B, denoted a b (or b a), pronounced "a and b" (or "b and a"), i.e., a b = as shown in Figure 1. Note that the more you merge, the more you merge, which is the opposite of what happens with intersections.

Characteristic: Deterministic given a set, any element that belongs to or does not belong to the set must be one or the other, and no ambiguity is allowed.

Heterogeneity: In a set, any two elements 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.

u is sum: that is, union.

Union definition: A set of all elements belonging to set A or to set B, denoted a b (or b a), pronounced "a and b" (or "b and a"), i.e. a b=

It is an intersection, neither nor or, but a common part of both.

Intersection Definition: A set of identical elements that belong to a and belong to b, denoted a b (or b a), pronounced "a intersect b" (or "b intersect a"), i.e. a b =

U is the union and can be called the sum of the two you say, and N is the intersection, which is something that has both.

p q is p or q, p q is p and q.

The meaning of is and is equivalent to the intersection in the set, the truth or falsity of the proposition p q is related to the truth or falsity of p and q, when p and q are all true propositions, the proposition p q is a true proposition, and everything else is a false proposition.

It is the meaning of the sharp or the equivalent of the union in the set, the truth or falsity of the proposition p q is also related to the truth or falsity of p and q, when p and q are all false propositions, the proposition p q is a false proposition, and everything else is a true proposition.

Grass. 1st floor, sorry to write like this, so sorry

A proposition is completely antithetical to its negative form. There is only one and only one between the two.

In mathematics, the method of counterproof is often used, and in order to prove a proposition, it is only necessary to prove that its negative form is not true.

How to get the negative form of a proposition?If you learn mathematical logic, it will be easy to understand, but now it can only be understood like this:

Original proposition: The square of all natural numbers is positive.

The standard form of the original proposition: any x, (if x is a natural number, then x is a positive number).

"Arbitrary" is the qualifier, "x is a natural number" is a condition, and "x is a positive number" is the conclusion. To deny a proposition, one needs to deny both its qualifier and its conclusion. The qualifiers "arbitrary" and "exist" negate each other.

Negative form: not (arbitrary x, (if x is a natural number, then x is a positive number)) x exists, (if x is a natural number, then x is not a positive number).

To put it another way: at least one natural number is not squared positively.

Whereas, the negative proposition of a proposition is used less. Whether a proposition is true or not has nothing to do with whether its negative proposition is true.

It's easy to get a negative proposition for a question, just deny the qualifiers, conditions, and conclusions.

Original proposition: The square of all natural numbers is positive.

The standard form of the original proposition: any x, (if x is a natural number, then x is a positive number).

Negative proposition: x exists, (if x is not a natural number, then x is not a positive number).

To put it another way: there is an unnatural number whose square is not positive.

Also, for inverse propositions, the negation qualifier is given, and then the conditions and conclusions are exchanged.

The inverse proposition of the proposition in the question is: there is x, (if x is a positive number, then x is a natural number).

The inverse of the negative proposition is the negative proposition of the inverse proposition, or the inverse proposition of the negative proposition, that is, the determinant does not change, negates the condition and the conclusion and exchanges.

The inverse of the proposition in the question is: any x, (if x is not positive, then x is not a natural number).

[Or] just one of the two is true.

And] both must be true, and one is indispensable.

i don't can't help want help you,but i don't ,sorry sorry.

I do not know. I can't help you enough. I'd love to help you, but I don't know. I'm sorry, I'm sorry, I'm sorry. ）

1. Indicate the intersection.

In set theory, let a and b be two sets, and the set composed of all the elements that belong to set a and belong to set b is called the intersection of set a and set b. i.e.: a b= .

Written as a b, it is read as "the intersection of a and b".

2. Represent union.

If a and b are sets, then a and b unions are sets with all the elements of a and all of b and no other elements. The union of a and b is usually written"a∪b", pronounced "a and b", is expressed in symbolic language, i.e.: a b = formally, x is an element of a b, if and only if x is an element of a, or if x is an element of b.

Dear, that's intersection and union, and the set part of mathematics is a unique symbol.

Intersection: The opening is downward, which means to take the common part.

Union: The opening is upward, which means to integrate all the elements in the two sets.

In mathematics, it is used to mean the union of two sets between two sets, and it is used to indicate the intersection of two sets between two sets, which can also be said to be the coincidence part of two sets.

is a union symbol in a collection.

is an intersection symbol in a set.

Let's see what others have to say.

Down is the intersection, which is the common part of the two sets, and up is the union, which is the sum of the two sets.

The former is to find the intersection, and the latter is to find the union, the intersection is the common part of the two sets, and the union is the sum of all the elements in the two sets.

One is union and the other is intersection.

The first intersection refers to the part that is common to both. The second union refers to all the parts of the sum of the two.

The first intersects, and the second is union.

The former is a union, and the latter is a complement.

The first is intersection.

The second is union.

And and or both play the role of connecting the two conditions, thus forming a large condition. Their differences are:

1、"And"It means that only when both conditions are met can it be counted as satisfying the major condition.

For example: 0 For example:

x=0 can only satisfy the second condition, but not the first condition, so the major condition cannot be satisfied;

x=1 satisfies both the second and second conditions, and it satisfies the large condition;

x=4 can only satisfy the first condition, but not the second condition, so it can't satisfy the big condition either;

x=10 means that the second condition cannot be satisfied, nor can the first condition be satisfied, so it cannot satisfy the major condition either;

In this way, 02,"or"It means that as long as any one of the two conditions can be met, it is considered to meet the major condition.

For example: 0 For example:

x=0 satisfies the second condition, i.e. it satisfies the large condition;

x=1 satisfies both the second and second conditions, and of course it satisfies the major condition;

x=4 satisfies the first condition, so it can also satisfy the big condition;

x=10 means that the second condition cannot be satisfied, nor can the first condition be satisfied, so it cannot satisfy the major condition;

In this way, 0< combination of x<5 or x<3 is exactly the same as x<5. (The big condition is the part of the two conditions that are all combined) < p>

1. The meaning of the representation is different:

1) "And" indicates an intersection.

2) "or" indicates union.

2. The meaning is different

1) "And" is and or equivalent, and if one of the two propositions is false, the new proposition is false.

2) "Or" is or, one of the two propositions is true, and the new proposition is true.

For example: 1. "Or" is a choice, choose one of the two, such as "tall or handsome", as long as one of the two conditions of "high" and "handsome" is met.

2. "And" is both, such as "tall and handsome" means "tall and handsome", and "and" means equivalent to "and".

"Or" means one of the two, "or: connect several possible events, indicating a choice relationship." "For example, if you say that I am studying English or math today, then you can only choose the same choice between learning English and math.

Sometimes when solving equations, there will be x=1 or x=2, where x=1 or x=2, which is true when it is equal to 1 and true when it is equal to 2, and "the meaning of co-existence," and connects several simultaneous events to indicate a common relationship. "For example, if you ask for leave today and tell the leader that you have a broken foot and a cold, then you have both things, both a broken foot and a cold.