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.
Hey!
So the first thing we realize is that it says that the equation is perpendicular to the line, meaning that the slope of the line is the negative reciprocal of the slope of the line you are given. Since we are given the slope of this line as 3/4 we can take the negative reciprocal of this to get -(4/3).
Now that we have the slope and a point on the line you can plug those into the equation y = mx + b to find b. The slope of the line is m and the point contains the x and y values.
5 = -(4/3)(-3) + b
5 = 4 + b
1 = b
Since we have the y-intercept and the slope now we can plug that into the slope-intercept form equation to get the equation we need:
y = -(4/3)x + 1
................................................................
Answer is A
Over which interval(s) is the function decreasing?
