Answer:
O U ⊆ A ∪ B True
O U ⊆ A ∩ B False
O A ∪ B ⊆ U True
O B ⊆ U True
O A ⊆ U True
O A ∩ B ⊆ U True
Step-by-step explanation:
To prove the first part
Remember that any set is a subset of the universal set. Therefore it is true that
Now, given any 
it is true that
Now according to the information given initially
And then you know that
Therefore 
and using double inclusion
.
Now using the information just exposed
O U ⊆ A ∪ B True
O U ⊆ A ∩ B False
O A ∪ B ⊆ U True
O B ⊆ U True
O A ⊆ U True
O A ∩ B ⊆ U True
Answer:
f(-2) = 2 and f(0) = 0.
Step-by-step explanation:
The piece wise function is given by, f(x) = x³ for x ≠ - 2 and f(x) = |x| for x = - 2.
Now, as defined above at x = -2, f(x) = |- 2| = 2
So, f(-2) = 2
Again, at x = 0, f(x) = x³ = (0)³ = 0.
So, f(0) = 0.
Hence, f(-2) = 2 and f(0) = 0. (Answer)
Answer:
5
Step-by-step explanation:
Answer:
(x, y) = (1, 1)
Step-by-step explanation:
Using the second equation to substitute for y in the first equation, we have ...
x = -2x +3
3x = 3 . . . . . . . add 2x
x = 1 . . . . . . . . .divide by 3
y = x = 1
The solution is (x, y) = (1, 1).
_____
If you have the graph, you can read the solution from it as the coordinates of the point where the lines cross.
