Given that P is equal to {0,1}, P is a set or an element

Given that P is equal to {0,1}, P is a set or an element

P is a set

Given the set M = {a ^ 2, a}, P = {- A, 2a-1} and the number of elements of M ∪ P is equal to 3, find m ∩ P!
Given the set M = {a ^ 2, a}, P = {- A, 2a-1} and the number of elements of M ∪ P is equal to 3, find m ∩ P!

① When a ^ 2 = - A,
a^2=-a
a1=0,
a2=-1.
Then when a = 0,
M={0,0},P={0,0}
So give up
When a = - 1,
M={1,-1}
P={1,-3}
M∪P={1,-1,-3},
M∩P={1}
② When a ^ 2 = 2a-1
(a^2-2a+1)=0
(a-1)^2=0
a=1
Then M = {1,1}
So give up
From ① and ②,
M∩P={1}

Given the set M = {X / 1 is less than or equal to x, less than or equal to 10, X belongs to n}, for its nonempty subset a, multiply every element K in a by (- 1) k power to find the sum, for example: a = {1,3,6}, the sum can be (- 1) X1 + (- 1) 3 power X3 + (- 1) 6 power X6 = 2, then for all nonempty subsets of M, find the sum

M={x| 1≤x≤10,x∈N }
= { 1,2,3,4,5,6,7,8,9 }
number of non empty subset of M = 2^9 -1
= 511
9C1+9C2+9C3+...+9C9 = 511
number of elements in all those non-empty subset of M
= (1)9C1 + (2)9C2+(3)9C3+...+(9)9C9
= 9 + 2(36) + 3(84)+4(126)+5(126)+6(84)+7(36)+8(9) +9(1)
= 9 +72+ 252+ 504+ 630+ 504+ 252+72+9
= 2304
Number of "1" appears in all those non-empty subet
=Number of "2" appears in all those non-empty subet
=...
=Number of "9" appears in all those non-empty subet
=2304/9 = 256
Sum of sum
=256( -1+2 - 3 +4 -5+6-7+8-9)
= 256(-5)
= -1280

The description method is used to represent the set of numbers divided by 3 and 1,

Enumeration {1,4,7,10,...}
Description {x | x = 3K + 1, K ∈ n}

To express "a set of positive integers divided by three and remaining one" by descriptive method:______ ．

Solution; ∵ all positive integers divided by 3 and remaining 1 can be written in the form of integral multiple of 3 plus 1, that is, x = 3K + 1, K ∈ n, the description method is used to express the set of positive integers divided by 3 and remaining 1: {x| x = 3K + 1, K ∈ n} so the answer is: {x| x = 3K + 1, K ∈ n}

The set of numbers divided by 9 and 2 can be expressed as?

{x | x = 9N + 2, n belongs to Z}

The set of numbers divided by 7 and 1 can be expressed as

x|x=7k+1（k∈z）

How to describe the set of integers divided by 3 and remaining 2

{y | y = 3x + 2, X is an integer}

The set of integers divided by 9 and 2 can be expressed as_______

{x|x=9k+2,k∈Z}

It is a set of integers divided by 6 and 1, 4 and 3,

31,43