Set theory

Question

Justify your answer with valid reason

$\phi \epsilon \left \{ A \right \} \wedge \phi \subseteq \left \{ A \right \}$

Where A is an non empty set $\left | A \right | \neq 0$

Comments

The answer should be T/F ?

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yes T/F and how you conclude some book or reference where it is written

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phi belongs to A will be true if element phi is present in the set, otherwise false. phi subset of A is always true.
Ans can be true or false. In general false.

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Just want to confirm i have read somewhere that $\phi$ is an natural element of all set if it is true this equation can hold true but i am not getting where i have read it

Answer 1

It is possible if A is a power set of some finite set . Because

1) ϕ ϵ {A} says "Phi is an element of set A" which is possible if A contains ϕ as an element (E.g A is power set)

2) ϕ ⊆ {A} . This is a universal truth for any set A. See this . 

Comments

Yes so it can be True, False both

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yes depends on A