0 votes 0 votes Justify your answer with valid reason $\phi \epsilon \left \{ A \right \} \wedge \phi \subseteq \left \{ A \right \}$ Where A is an non empty set $\left | A \right | \neq 0$ Set Theory & Algebra set-theory&algebra set-theory + – Tesla! asked Apr 2, 2017 • recategorized Jul 7, 2022 by Lakshman Bhaiya Tesla! 642 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply prasitamukherjee commented Apr 3, 2017 reply Follow Share The answer should be T/F ? 0 votes 0 votes Tesla! commented Apr 3, 2017 reply Follow Share yes T/F and how you conclude some book or reference where it is written 0 votes 0 votes prasitamukherjee commented Apr 3, 2017 reply Follow Share 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. 0 votes 0 votes Tesla! commented Apr 3, 2017 reply Follow Share 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 0 votes 0 votes Please log in or register to add a comment.
Best answer 1 votes 1 votes 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 . Heisenberg answered Apr 3, 2017 • selected Apr 5, 2017 by Tesla! Heisenberg comment Share Follow See all 2 Comments See all 2 2 Comments reply prasitamukherjee commented Apr 3, 2017 reply Follow Share Yes so it can be True, False both 0 votes 0 votes Heisenberg commented Apr 3, 2017 reply Follow Share yes depends on A 0 votes 0 votes Please log in or register to add a comment.