Say the inverse proposition of the proposition "in the rectangular coordinate system, the point (x, y) and the point (- x, - y) are symmetrical about the origin", and judge the truth of the inverse proposition

Say the inverse proposition of the proposition "in the rectangular coordinate system, the point (x, y) and the point (- x, - y) are symmetrical about the origin", and judge the truth of the inverse proposition

Inverse proposition: in Cartesian coordinates, the two symmetrical points about the origin must be points (x, y) and (- x, - y)
This proposition is true

In the rectangular coordinate system, the proof that the coordinates of two symmetrical points about the origin are (x, y) and (- X. - y)

Let a point be a (x, y), and its symmetric point about the origin be B (a, b)
It is obvious that the origin is the midpoint of the point, that is, 0 = (x + a) / 2, 0 = (y + b) / 2
a = -x,b = -y
B(-x,-y)

If x ^ 2 + X ≤ 0, then l2x + 1L

Inverse proposition: if l2x + 1l0, then l2x + 1L > = 1 true proposition
Inverse negative proposition: if l2x + 1L > = 1, then x ^ 2 + x > 0 is false proposition
Conclusion: the original proposition and the inverse no proposition are equivalent propositions. If the original proposition is true, the inverse no proposition is true. The inverse proposition and the no proposition are equivalent propositions. If the inverse proposition is true, the no proposition is true

Write out: if x = 2, then x square + X-6 = 0 inverse proposition, no proposition, inverse no proposition and judge the truth
fast

If X & # 178; + X-6 = 0, then x = 2 false proposition
No proposition if x ≠ 2, then x & # 178; + X-6 ≠ 0 false proposition reason: when x = - 3, X & # 178; + X-6 = 0
If X & # 178; + X-6 ≠ 0, then x ≠ 2 is true proposition

Given the proposition "if x + 1 = 0, then the square of x-2x-3 = 0", write his inverse proposition, no proposition, inverse no proposition, and judge whether it is true or false

First of all, the true and false of the original proposition, the true proposition
The inverse proposition is to exchange the conditional conclusions of the original proposition: if x ^ 2-2x-3 = 0, then x + 1 = 0
Judging true or false: x ^ 2-2x-3 = 0, then x = - 1 or 3, obviously false proposition
No proposition: if x + 1 is not equal to 0, then x ^ - 2x-3 is not equal to 0
The original proposition is consistent with the converse proposition

Write the inverse proposition of "if the square of X is less than 4, then x is less than 2", no proposition, inverse no proposition, and judge the truth of the four propositions

Inverse proposition: if x is less than 2, then the square of X is less than 4 (true proposition); no proposition: if x's Square is greater than or equal to 4, then x is greater than or equal to 2 (false proposition); inverse proposition: if x is less than or equal to 2, then x's Square is greater than or equal to 4 (false proposition)

If the square of X + X is less than or equal to zero, then 12x + 11

It is known that the original proposition is "if X & sup2; + X ≤ 0, then 12x + 11

The inverse proposition of x = - 8 or x = 1 if x square + 7x-8 = 0

If x = - 8 or x = 1, then x squared + 7x-8 = 0

A proposition is equal to its converse proposition, negative proposition, converse proposition. In these four propositions, the number of true proposition and false proposition is equal, right?

Wrong
Because propositions and inverse propositions are true and false, and no propositions and inverse propositions are true and false, but propositions and no propositions can be true and false, and there can be true and false, so there may be four true, two true, two false and four false

What is the number of true propositions in the original proposition, inverse proposition, no proposition and inverse no proposition

There are three possibilities: 0, 2, 4 examples: 1. If x is greater than 5, then x is greater than 4. Original proposition is true, inverse proposition is false, no proposition is false, inverse proposition is true. There are two true propositions. 2. If x is greater than 5, then x is less than 3. Original proposition is false, inverse proposition is false, no proposition is false, inverse proposition is false