State the whether given statement is true or false
If $A$ is any set, prove that: $A \subseteq ϕ \Leftrightarrow A = ϕ$ .

True

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False

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Solution

The correct option is A True
Let $A \subseteq ϕ$
Now since $ϕ$ is subset of every set
therefore, $ϕ \subseteq A$ ---- (i)
also, $A \subseteq ϕ$ --- (ii)
From (i) ad (ii)
$A = ϕ$
Conversely, let $A = ϕ$
Implies that
$A \subseteq ϕ$
Therefore, $A \subseteq ϕ \Leftrightarrow A = ϕ$

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