9514 1404 393
Answer:
x = 5, y = 8, z = 19, w = 26
Step-by-step explanation:
You are given four equations in the four unknowns, so solution is not so difficult.
A ∪ B = x + y + z = 32
A ∩ B = y = 8
A = x + y = 13
A' ∪ B' = w + x + z = 50
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Subtracting the 2nd equation from the 3rd, we get ...
(x +y) -(y) = (13) -(8)
x = 5
Subtracting the third equation from the first, we get ...
(x +y +z) -(x +y) = (32) -(13)
z = 19
Filling in values for x and z in the last equation gives ...
w +5 +19 = 50
w = 26
In summary, ...
x = 5, y = 8, z = 19, w = 26
