The answer is: B.
1. First of all, the relationship between the range of sets P, Q, U and X is given in the stem, which is denoted as S.
2. The meaning of each option is that any X determined in the stem, that is, any element in S, must satisfy a certain formula.
As can be seen from the title, p and q are subsets of u; S is the remainder of u after removing the intersection of p and q. As can be seen from the figure, S can be divided into three parts, and the elements in each part have the same affiliation with P and Q, so you only need to analyze any one of the three parts as a representative. The three parts of S are:
① S 1: Its elements belong to P, but not Q;
② S2: Its element belongs to Q, but not to P;
③ S3: Its elements belong to neither P nor Q;
A: x? P and x? q；
First of all, we should understand the meaning of this sentence, which means that the above formula holds for any element X in S.
Obviously, this is wrong. The counterexample is easy to find: the elements in S 1 and S2 are all.
B: x? P or x q；
Like A, we must first understand its meaning, and then analyze the representative elements in S 1, S2 and S3.
① S 1:x？ Q, in line with the original proposition;
② S2:x？ P, also conforms to the original proposition;
③ S3:x？ P and x? Q, more in line with the original proposition;
To sum up, all the elements in S conform to this proposition, so option B is correct.
c:x∈CU(P∪Q)；
This set is the U left after the union of P and Q is removed. Obviously, it happens to be S3. Then, the result is obvious: the elements in S 1 and S2 do not belong to S3, so option C is wrong.
D:x ∈ cup;
This group is the remaining U after removing P, which happens to be S2∪S3. Similarly, since none of the elements in S 1 belong to S2∪S3, option D is also wrong.