This is impossible to answer without knowing what the sets A and B contain (and what ξ even refers to - universal set?).
However, we have
(A U B)' = A' ∩ B'
so that
(A ∩ B) U (A U B)' = (A ∩ B) U (A' ∩ B') = (A U A') ∩ (B U B')
If ξ is indeed the universal set, then both A U A' = ξ and B U B' = ξ, so we end up with ξ ∩ ξ = ξ.
True.
The y-axis of the f(x) must equal to the x-axis of g(x)
The x-axis of the f(x) must equal to the y-axis of g(x)
Answer:
7.) 7
10.) 0
Step-by-step explanation:
When it means "evaluate the function", it's in essence asking us to see what the function spits out when we feed it a certain input. Our inputs are our x values, which spit out a y value.
Evaluating the function when x = 1:
Let's look at where the function has an x value of 1. We see it near the bottom of the table and see the y value associated with the input is 7. So when the function is fed 1 as an input, it spits out 7.
Evaluating the function when f(x) = - 2:
This one is a weird because of the new notation. Just think of it as some value of f, which we don't know (so we represent it as an x-variable) must equal -2. So let's look at our table to find out where our output is -2. We find that when f(x) = -2 the input is 0. So the input which gives -2 is 0.
Answer:

Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(- 2, 5) and (x₂, y₂ ) = B(3, 8)
d = 
= 
= 
= 