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Pls help me with this set problem

Pls help me with this set problem-example-1

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(1) False.
\{0\}\in\mathscr{U} is saying "the set containing only 0 (that is, {0}) is an element of
\mathscr U", but this is not the case.
\mathscr U is the set containing only 0 and 1.

(2) True.
\{0\}\subset\mathscr{U} means "the set {0} is a subset of
\mathscr{U}". 0 itself is an element of
\mathscr U, so {0} is indeed a subset of
\mathscr U.

(3) True. 0 is clearly an element of
\mathscr U.

(4) False. This statement says "0 is a subset of
\mathscr U" but 0 itself is not a set, it's a number.

User Dharmendra Mishra
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