Question

31. The set ( AnB')'U(BnC) is equal to :
(a) A'U BUC
(b) A'UB
(c) A'UC
(d) AnB​

Answer 1

Given:

The set $(A\cap B')'\cup (B\cap C)$ is equal to.

To Choose:

(a) A'U BUC

(b) A'UB

(c) A'UC

(d) A $\cap$ B​

Solution:

let if possible, sets A, B and C are given such that-  A > B > C.

according to question;

$(A\cap B')'\cup(B\cap C)\\=(A'\cup (B')')\cup(B\cap C)\\=(A'\cup B)\cup (B\cap C)\\=A'\cup B$

since,

$(B')'=B \\and\\(A\cap B)'=(A'\cup B')$

Thus, (b) is correct option.