Let u = {positive integer no more than 5}, a = {x | x ^ 2-5x + q = 0}, B = {x | x ^ 2 + PX + 12 = 0}, (CUA) UB = {1,3,4,5}. Find P, Q, AUB I just learned the basic operation of set. The teacher left this question as a thinking question. I've read your explanation, but I still don't quite understand it

Let u = {positive integer no more than 5}, a = {x | x ^ 2-5x + q = 0}, B = {x | x ^ 2 + PX + 12 = 0}, (CUA) UB = {1,3,4,5}. Find P, Q, AUB I just learned the basic operation of set. The teacher left this question as a thinking question. I've read your explanation, but I still don't quite understand it

Complete set u = {positive integers no more than 5} = {1,2,3,4,5}
(CuA)UB={1,3,4,5}
So: a contains {2}, B does not contain {2}
Substituting {2} into a
2^2-2*5+q=0
q=6
A={X|X^2-5X+6=0}={X|(X-2)*(X-3)=0}={2,3}
CuA={1,4,5}
Then B contains {3}
Substituting: 3 ^ 2 + p * 3 + 12 = 0
p=-7
B={X|X^2-7X+12=0}={X|(X-3)*(X-4)=0}={3,4}
AUB={2,3,4}