1. ## doubt

Respected sir,
I hava the following doubt. please clarify my doubt.

let x belongs to {1}.
<=> x belongs to any one of the subsets of {1}.
<=> x=1 or x belongs to {}.
But generally every body will write
x=1 <=> x belongs to {1}.
But for to use <=> we should write:
x belongs to{1} and x does not belongs to {}.
Why dont every one write like this.

2. Originally Posted by ksssudhanva
Respected sir,
I hava the following doubt. please clarify my doubt.

let x belongs to {1}.
<=> x belongs to any one of the subsets of {1}.
Because this statement is not true. $\{ 1 \}$ has only one element. That is to say that $\emptyset \notin \{ 1 \}$. $\emptyset$ is indeed a subset of $\{ 1 \}$, but no element of this set is equal to $\emptyset$ because the empty set is not listed as one of the set members.

-Dan

3. Originally Posted by ksssudhanva
Respected sir,
I hava the following doubt. please clarify my doubt.

let x belongs to {1}.
<=> x belongs to any one of the subsets of {1}.
<=> x=1 or x belongs to {}.
But generally every body will write
x=1 <=> x belongs to {1}.
But for to use <=> we should write:
x belongs to{1} and x does not belongs to {}.
Why dont every one write like this.
Because for all x in A, A!={}, x is not in {}.

RonL