Question

phi is subset of every set....prove it...​

Answer 1

$\large \mathfrak \red{Given:-}$

$\: \: \: \: \: \: \tt{ \phi \: is \: subset \: of \: every \: set.} \\ \: \: \: \: \: \: \: \tt{prove \: it.}$

$\large \mathfrak \red{Solution:-}$

$\underline \blue{ \: \: \: \: Firstly. \: \: \: \: \: }$

$\: \: \: \tt{What \: is \: meaning \: of \: \red{\phi } \: in \: set \: ?}$

$\: \: \: \: \: \: \tt{ It \: is \: a \: type \: of \: set \: which} \\ \tt{ \: \: \: \: \: \: help \: to \: reorgan ize \: by } \\ \: \: \: \: \: \: \tt{ emply \: or \: null \: set \: denoted } \\ \: \: \: \: \: \: \tt{ by \: \phi\: or\: \{\}.}$

$\tt{Let \: \underline{Case \: 1.}}$

$\tt{A= \{a,b \} \: \: \: \: \: \: \: where \: as \: {2}^{n} \implies 4.}$

$\tt{A= \{ \{a \} \{b \} \{a,b \} \{ \} \}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \tt{A \subset \phi}$

$\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt { \red{H}ance \: \red{P}roved.}$

Answer 2

Answer:

yes ,phi is subset of every set

because phi is a empty (or) void set

empty set will contain no elements

EX: take A={1,2}

and B={ }

set B is subset of A unless there is some element in B that is not in A

if B is not a subset of A then there is a element in set B,but B has no elements Hence this is a contradiction,

there fore phi or null set is a empty set of every set