If the set a = {x | x ^ 2 + X-6 = 0}, B = {x | MX + 1 = 0}, B is the proper subset of a, the value of M is obtained

If the set a = {x | x ^ 2 + X-6 = 0}, B = {x | MX + 1 = 0}, B is the proper subset of a, the value of M is obtained

x^2+x-6=0
(x+3)(x-2)=0
x1=-3 x2=2
So a = {- 3,2}
If B is a proper subset of a, then
The solution of MX + 1 = 0 is x = - 3 or x = 2
therefore
-3M + 1 = 0, M = 1 / 3
2m + 1 = 0, M = - 1 / 2

1. Given the set a = {x | x ^ 2 + X-6 = 0}, B = {x | MX + 1 = 0}, if a ∪ B = a, find the set M composed of real number M
2. Given the set a = {x | x ^ 2-3x-10 ≤ 0}, B = {x | m + 1 ≤ x ≤ 2m-1}, if a ∩ B = B, find the value range of real number M

Well, there's no difference
1. For a = - 3 or 2, let a contain B
If B is an empty set, then M = 0
If B is not empty, then M = 1 / 3 or - 1 / 2
So m = {0,1 / 3, - 1 / 2}
2 means a contains B
Obviously, when B is an empty set:
m＜2
If not empty
For a = - 2 or 5
M + 1 ≤ - 2 2m-1 ≥ 5 no solution
So to sum up, m < 2

Mathematical set problem: a = {x | x ^ 2-5x + 6 = 0}, B = {x | MX = 1}, if set B is the true subset of a, find the set M composed of real number m, and write all subsets of M

M = {1 / 3,1 / 2}, subsets are: empty set, {1 / 3}, {1 / 2}, {1 / 3,1 / 2}

Let a = {x | x ^ 2-5x + 6 = 0}, B = {x | mx-6 = 0} and B be a subset of a to find M

A = {x | x ^ 2-5x + 6 = 0}, we can see that a = {2,3}
If B is a subset of a, then B may be:
{} ,{2} ,{3} ,{2,3}
B = {x | mx-6 = 0}
When m = 0, B is an empty set
When m! = 0, x = 6 / m
If x = 2, M = 3
If x = 3, M = 2
To sum up, M = 0, 2, 3

If M = {x | x ^ 2 + 3x-6 = 0} n = {x | KX + 6 = 0} and N is a proper subset of M, then the product of all possible values of K is

Because the discriminant of equation x ^ 2 + 3x-6 = 0 = 9 + 24 > 0, m ≠Φ,
Because n is a proper subset of M,
So n may be an empty set, where k = 0,
Then the product of all possible values of K must be 0

Let m = {x m}

Choose C
The length of M is 2 / 3 and that of n is 1 / 2
The minimum value of "length" of M ∩ n is
2/3+1/2-1=1/6

Let m = {x | m ≤ x ≤ m + 34}, n = {x | N-13 ≤ x ≤ n}, and m and N are subsets of {x | 0 ≤ x ≤ 1}. If B-A is called the length of {x | a ≤ x ≤ B}, then the minimum value of the length of M ∩ n is ()
A. 112B. 23C. 13D. 512

According to the meaning of the question, the length of M is 34, and the length of n is 13. When the length of M ∩ n is the minimum, m and n should be at the left and right ends of the interval [0,1], so the minimum length of M ∩ n is 34 + 13-1 = 112, so a

If we know the interval [M, n], the interval length is N-M, the set a and B are subsets of [0,1], the interval length of set a is 2 / 3, and the length of set B is 3 / 4, then the minimum length of set a ∩ B is obtained

In order to minimize the length of area a ∩ B of the set, the area of a ∩ B should be as small as possible, that is, a and B should be as far away from each other as possible, each on one side
(it's better to draw a picture)
Then the minimum length of a ∩ B is 2 / 3 + 3 / 4-1 = 5 / 12
If you don't understand, please hi me, I wish you a happy study!

Let a = {(x, y) | 3x + 2Y = 5}, B = {(x, y) | 4x-y = 3}, find a ∩ B

A∩B=｛（1,1）｝

Given the set a = {(x, y) | 2x-3y + 1 = 0}, B = {(x, y) | 3x-2y-1 = 0}, find a ∩ B

A∩B={（1,1）}