# Reflexive, Symmetric, Transitive, and Substitution Properties

Reflexive Property

The Reflexive Property states that for every real number $x$, $x=x$.

Symmetric Property

The Symmetric Property states that for all real numbers $x\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}y$,

if $x=y$, then $y=x$.

Transitive Property

The Transitive Property states that for all real numbers $x\text{\hspace{0.17em}},y,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}z,$

if $x=y$ and $y=z$, then $x=z$.

Substitution Property

If $x=y$, then $x$ may be replaced by $y$ in any equation or expression.