Q23

MCQ1 mark, −0.33

Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$ . For any $T \in U$ , let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$ . For any $T, R \in U \text{ let } T \backslash R$ be the set of all elements in $T$ which are not in $R$ . Which one of the following is true?

(A)

$\forall X \in U, (|X| = |X'|)$

(B)

$\exists X \in U, \exists Y \in U, (|X| = 5, |Y|=5$ and $X \cap Y = \phi)$

(C)

$\forall X \in U, \forall Y \in U, (|X| = 2, |Y|=3$ and $X \backslash Y = \phi)$

(D)

$\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$

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