How to prove that the original proposition has the same truth or falsity as its inverse negative pro

It is proved wrong by the method of counterproof, because the principle of the principle of the establishment of the method of counterproof is that the inverse proposition is equivalent to the original proposition.

In fact, this thing can be considered an axiom. It is equivalent to the axiom "law of exclusion".

Our mathematical system is based on these axioms.

The law of exclusion is one of the basic laws of traditional logic. It is usually stated that A is B or not B. Traditional logic first regards the law of exclusion as the law of things, which means that any thing has a certain property or does not have a certain property at the same time, and there is no other possibility.

The law of exclusion is at the same time the law of thinking, i.e., whether a proposition is true or not, and there is no other possibility. The law of exclusion is also a normative law of epistemic activity, which means that no one should deny a proposition (a) and its negation (not a) at the same time, that is, there can be no two arguments about a proposition and its negation. The law of exclusion is also regarded as a law of logical semantics, that is, any word or sentence should express a certain idea or not express that idea in the same context.

As the latter two laws, it is also called the requirement of the law of exclusion. The law of exclusion does not exclude that there are intermediate links in the development of specific things, as well as multiple states and possibilities. In modern logic, a a (reads:

a or not a), which is the embodiment of the law of exclusion in propositional logic; "x(f(x) f(x)) (read: x has or does not have a property f for any individual x) is the embodiment of the law of exclusion in predicate logic. Since the logic of construction does not admit the existence of real infinity in the real world, but only admits that infinity is a process, therefore, in this logic, the law of exclusion does not hold when it comes to infinite objects; Proving the existence of a proposition by counterproof is also not a valid method of proof.

Using the method of counterproof, the original proposition is "if p then q", then the inverse negative proposition is "if not q then not p".

Assuming that "the original proposition has the same true or false nature as its inverse negative proposition", there is an error of "if p q is true, then non-q and non-p are false".

or "if p q is false, then non-q is not p is true".

1. If p q is true, then non-q non-p is false.

Because non-q is not p is false, then non-q p is true This contradicts p p q is true 2, and if p q is false, then non-q is not p true.

Because p q is false, p non-q is true This contradicts non-q and non-p is true, so the assumptions are not true, so the original proposition has the same true or false nature as its inverse negative proposition, which can be proven.

The principle of the establishment of the counter-proof method is that the inverse negative proposition is equivalent to the original proposition?

What are you talking nonsense?

The method of refutation is to exclude all other possibilities, leaving only this one possibility, which has nothing to do with the equivalence of the inverse proposition and the original proposition.

Not necessarily, because false propositions are partially wrong.

For example, the false proposition "irrational numbers, irrational numbers, irrational numbers". The counter-example is "(let a be an irrational number) a+(-a) 0" but there is also a part of the pair, "a+a=2a". So it's not necessarily the other way around.

The interrelation of the four propositions:

Original proposition vs. inverse proposition.

Reciprocal reverse, no oak rock Qi proposition and original proposition mutual negation, original proposition and inverse negative proposition.

Reciprocal negation, inverse proposition or negative proposition inverse negation, inverse proposition and inverse negative proposition mutual negation, inverse negative proposition and negative proposition inverse to each other.

Proposition conditions. Sufficiency and necessity.

1. "If p, then q" is a true proposition.

It is called the introduction of q from p, which is denoted as p=>q, and says that p is a sufficient condition for q.

Q is the necessary condition of P.

2. "If p, then q" is a false proposition, which is called the inference of q from p, which is denoted as p≠ q, and says that p is not a sufficient condition of q (or p is a non-sufficient condition of q), and q is not a necessary condition of p (or q is a non-necessary condition of p).

Sufficient conditions. If there is both p=>q and q=>p, it is denoted as p<=>q, and p is said to be a sufficient and necessary condition for q.

or q is a sufficient and necessary condition for p), and the simple jujube is called a sufficient and necessary condition, and it can also be called the equivalence of p and q.

Using the method of counterproof, the original proposition is "if p then q", then the inverse negative proposition is "if not q then not p".

Assuming that "the original proposition has the same true or false nature as its inverse negative proposition", there is an error of "if p q is true, then non-q and non-p are false".

or "if p q is false, then non-q is not p is true".

1. If p q is true, then non-q non-p is false.

Because non-q non-p is a brother's feast leave, then non-q p is true This contradicts p p q is true 2, if p q is false, then non-q non-p is a true cave friend.

Because p q is false, p non-q is true This contradicts non-q and non-p is true, so the assumptions are not true, so the original proposition has the same true or false nature as its inverse negative proposition, which can be proven.

You can also use a truth table, that is, a truth value that defines exhaustive a, b. There are four scenarios:

1) A is true, B is true. Rule.

a b is true; b a is true.

2) A is true, B is false. Rule.

a b is false; b a is false.

3) A is false, B is true. Rule.

a b is true; b a is true.

4) A false, B false. Rule.

a b is true; b a is true.

So, in any case, there is always p = qThat is, a proposition is equivalent to its inverse proposition. Also written as:

p ←→q.,9,

The true and false relationships of the original proposition, the negative proposition, the inverse proposition and the inverse negative proposition are as follows:

Let the two propositions be inverse to each other, and they have the same true or false properties. Let two propositions be mutually inverse propositions or mutually negative propositions, and their truth and falsehood have no relationship, the original proposition and the inverse proposition are the same true and false, and the inverse proposition and the negative proposition are the same true and false.

A declarative sentence that can judge true or false is called a proposition, a correct proposition is called a true proposition, and a false proposition is called a false proposition. The original proposition and the inverse proposition are mutually reverse, the negative proposition and the original proposition are mutually negative, the original proposition and the inverse proposition are inversely negative to each other, the inverse proposition and the inverse proposition are mutually reverse, the inverse proposition and the inverse proposition are mutually reverse, and the inverse proposition and the negative proposition are mutually reverse.

The four propositions refer to the original proposition, the inverse proposition, the negative proposition and the inverse negative proposition, and the interrelationship of the four propositions will be shared with you for reference. The interrelationship of the four propositionsThe interrelationship of the four propositions: the original proposition and the inverse proposition are inverse, the negative proposition is reciprocal to the original proposition, the original proposition and the inverse proposition are inverse to each other, the inverse proposition is inverse to the inverse, the inverse proposition is inverse to the inverse, the inverse proposition is inverse to the inverse proposition, the inverse proposition is inverse to the inverse proposition.

The relationship between the truth and falsehood of the four propositions: The two propositions are inverse and negative propositions of each other, and they have the same truth or falsehood. Two propositions are mutually inverse propositions or mutually negative propositions, and their truth and falsehood have no relationship (the original proposition and the inverse proposition are the same as the true and false, and the inverse proposition and the negative proposition are the same true and false) The form of the proposition 1. For two propositions, if the conditions and conclusions of one proposition are the conclusions and conditions of the other proposition, then these two propositions are called reciprocal propositions, and one of the propositions of the object hole is called the original proposition, and the other proposition is called the inverse proposition of the original proposition.

2. For two propositions, if the conditions and conclusions of one proposition are the negation of the conditions of the other proposition and the negation of the conclusion respectively, then these two propositions are called mutually negative propositions, one of which is called the original proposition, and the other proposition is called the negative proposition of the original proposition. 3. For two propositions, if the entry of one proposition [ooo

The simplest way is to use a list of truth values, that is, to define the truth values of exhaustive a and b. There are four kinds of shouting positive sales: 1) A is true, B is true.

then a mu is boring b is true; b a is true. 2) A is true, B is false. then a b is false; b a is false.

3) A is false, B is true. then a b is true; b a is true. 4) A false, B false.

then swift and bent a Zheng You b is true; b a is true. So, in any case of pruning, there is always p=q. That is, a proposition is equivalent to its inverse proposition. Also written as:

First of all, the original proposition and its negative proposition are not necessarily opposed to the truth or falsehood of the proposition, and should be irrelevant. 1.When the original proposition is true, its negative proposition can be false.

For example, the original proposition: If a polygon is a quadrilateral, then the sum of the outer angles of this polygon is 360;Negative proposition: If there is a polygon that is not a quadrilateral, then the sum of the outer and inner angles of this polygon is not True when the original proposition is true, its negative proposition can also be true.

For example, the original proposition: If a wild polygon is a quadrilateral, then the sum of the inner angles of this polygon is 360;Negative proposition: If there is a polygon that is not a quadrilateral, then the sum of the inner angles of this polygon is not If the original proposition is false, its negative proposition can be true.

For example, the circular proposition: If there is a polygon that is not a quadrilateral, then the sum of the outer and inner angles of this polygon is not 360;No proposition: If a polygon is a quadrilateral, then the sum of the outer angles of this Zhengji polygon is 360.

That is, the original proposition and the inverse negative proposition of the original proposition.

True or false

The original proposition is equivalent to its inverse negation

For example, there are propositions, isotope angles.

Equal, two straight lines are parallel, and its inverse negative proposition is: the two straight lines are not parallel, and the isotopic angles are not equal Obviously, you can tell that the second proposition is a true proposition.

That's right, and we say you give me the proposition: the angles are equal, the two straight lines are parallel You can't judge the proposition: the angles are not equal, the two lines are not parallel Although we all know that the second proposition is true, why can't we judge it?

Because the relationship between the original proposition and its negative proposition (not the reverse negative) is not the same as the truth or falsehood, I have forgotten what the relationship should be