Question

Pls help me with this set problem

Answer 1

(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.