EDB — 2DK

[2DK]Let $(X,{𝜏}_X)$ be a topological space, $Y\subseteq X$ the topological space with the induced topology

Fix $E\subseteq Y$, consider these statements.

(cX)

$E$ is a connected set in the topological space $(X,{𝜏}_X)$;

(cY)

$E$ is a connected set in the topological space $(Y,{𝜏}_Y)$.

Are the two statements equivalent?