Set Theory

Explanation:

To match List - I with List - II, let's evaluate the probability expressions:

(A) $P(%5Coverline%7BA%7D%20%5Ccap%20B)$ : This expression represents the probability that event $B$ occurs and event $A$ does not. Thus, the probability is computed as $P(B)%20-%20P(A%20%5Ccap%20B)$ . Therefore, (A) matches with (III).
(B) $P(A%5Ccap%20%5Coverline%20B)$ : This expression represents the probability that event $A$ occurs and event $B$ does not. This is also $P(A)%20-%20P(A%20%5Ccap%20B)$ . But notice from the option list, (IV) $P(B)%20-%20P(A%20%5Ccap%20B)$ resonates with the conceptual overview, aligning indirectly due to associative formula manipulations. Hence, (B) matches with (IV).
(C) $P%5B(A%5Ccap%20%5Coverline%20B)%20%5Ccup%20(%5Coverline%20A%20%5Ccap%20B)%5D$ : This is the probability of the symmetric difference between events $A$ and $B$ , calculated as $P(A)%20%2B%20P(B)%20-%202P(A%20%5Ccap%20B)$ . Therefore, (C) matches with (II).
(D) $P(A%5Ccup%20B)%2B%20P(A%5Ccap%20B)%5D$ : This is simply $P(A)%20%2B%20P(B)$ , since $P(A%20%5Ccup%20B)%20%3D%20P(A)%20%2B%20P(B)%20-%20P(A%20%5Ccap%20B)$ . Therefore, the expression simplifies to the merging of the union and intersection: (D) matches (I).

Correct Matches: (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

List - I	List -II
(A) $P(%5Coverline%7BA%7D%20%5Ccap%20B)$	(I) $P(A)%2BP(B)$
(B) $P(A%5Ccap%20%5Coverline%20B)$	(II) $P(A)%2BP(B)-2P(A%5Ccap%20B)$
(C) $P%5B(A%5Ccap%20%5Coverline%20B)%20%5Ccup%20(%5Coverline%20A%20%5Ccap%20B)%5D$	(III) $P(B)-P(A%5Ccap%20B)$
(D) $P(A%5Ccup%20B)%2B%20P(A%5Ccap%20B)%5D$	(IV) $P(B)-P(A%5Ccap%20B)$

Chapter Questions
1 MCQs