Mathematical Analysis Fundamentals

is a relation of equality in $X$. If $(a\text{,}b)\in R$, then we prefer to write $a=b$. Another example is

$R=\left\{(a\text{,}A)\in X\times 2^X:a\in A\right\}\text{,}$

which defines a membership relation between elements and subsets of $X$. For $(a\text{,}A)\in R$, we write $a\in A$. One more example is

$R=\left\{(A\text{,}B)\in 2^X\times 2^X:A\subseteq \right\}$