A set [tex]X[/tex] is closed under multiplication if for any two elements of [tex]X[/tex], say [tex]a,b\in X[/tex], we also have their product [tex]ab\in X[/tex]. ([tex]a[/tex] and [tex]b[/tex] can be the same element)
The set [tex]C=\{0,1,3\}[/tex] is not closed, because 3*3=9 does not belong to [tex]C[/tex].
