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 $T$, $R \in U$, let $T\text\R$ be the set of all elements in $T$ which are not in $R$.Which one of the following is true?

Question

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 $T$, $R \in U$, let $T\text\R$ be the set of all elements in $T$ which are not in $R$.Which one of the following is true?

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

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

TuteeHUB · Answer

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

TuteeHUB · Answer

$\exists X \in U \text{ } \forall Y \in U (|X|=2,|Y|=3) \text{ and }(X\text\Y = \phi )$

TuteeHUB · Answer

$\forall X\in U\text{ }\forall Y\in U (X\text\Y=Y'\text\X')$

1.	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 \(T\), \(R \in U\), let \(T\text\R\) 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.	\(\exists X \in U \text{ } \exists Y \in U (\|X\|=5,\|Y\|=5) \text{ and }(X\cap Y = \phi )\)
C.	\(\exists X \in U \text{ } \forall Y \in U (\|X\|=2,\|Y\|=3) \text{ and }(X\text\Y = \phi )\)
D.	\(\forall X\in U\text{ }\forall Y\in U (X\text\Y=Y'\text\X')\)
Answer» E.

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