Given that a = {1,4, X}, B = {1, x ^ 2}, and a intersects B = B, find the value of X and set B

Given that a = {1,4, X}, B = {1, x ^ 2}, and a intersects B = B, find the value of X and set B

A intersects B = B, that is, B is a subset of a, that is to say, all elements in set B must appear in set A. now there are only two possibilities: 1) x ^ 2 = 4, the solution is x = 2, a = {1,4,2}; b = {1,4} or x = - 2, a = {1,4, - 2}; b = {1,4} 2) x ^ 2 = x, the solution is x = 0 or 1

Set a = {4, a square, B-2} B = {1,2, a, a + B}, a intersection B is 1,4, find the value of a and B

A ∩ B = {1,4}, so both a and B contain elements 1,4
Consider a
If B-2 = 4, then B = 6, then B = {1,2, a, a + 6}, then a = 4 or a + 6 = 4 in B
If a = 4, then B = {1,2,4,10}, a = {1,16,4}, which is consistent with
If a + 6 = 4, then a = - 2, a = {1,4,4}, there are repeated elements, which do not conform to the definition of set
If a ^ 2 = 4, then a = 2 or - 2,
If a = 2, then B = {1,2,2 + a}, there are repeated elements, which do not conform to the definition of set
If a = - 2, then B = {1,2, - 2, - 2 + B}, in order to make B have element 4, we need to have - 2 + B = 4, but at this time, the elements in a repeat, which is inconsistent
A = 4, B = 6

Let a = {- 3}, B = {x | ax 1 = 0}, a ∩ B = B, find the value of A
Let a = {- 3}, B = {x | ax + 1 = 0}, a ∩ B = B, find the value of A

A∩B=B
When B is
ax+1=0
a=0
When B is not
A∩B=B
A={-3}
B={x|ax+1=0}
-3 is the element in B
-3a+1=0
a=1/3
The value of a = 0 or 1 / 3