Connected Set in Subspace

Theorem
Let $T = \struct{S, \tau}$ be a topological space.

Let $A \subseteq B \subseteq S$.

Let $T_B = \struct{S, \tau_B}$ be the topological space where $\tau_B$ is the subspace topology on $B$.

Then
 * $A$ is connected in $T_B$ $A$ is connected in $T$.