$S_1$ : function $f:[a,b]\to R$  defined by $f\left(x\right)={(x-a)}^2{(x-b)}^2+x,$takes the value  $\frac{a+b}{2}$ for some  $x\in [a,b]$
$S_2:$If a function $y=g\left(x\right)$  is defined on $[a,b]$  and continuous on $(a,b)$ , then for any $k\in (g\left(a\right),g\left(b\right))$ there is some point  $c\in (a,b)$ such that  $g\left(c\right)=k$