How is implication same as entailment
Let $\varphi$ and&nbsp;$\psi$ be formulas of propositional logic. We write, as Norvig says, $\varphi\vDash \psi$ iff $M(\varphi)\subseteq M(\psi)$: that is, iff every truth assignment that makes $\varphi$&nbsp;true also make $\psi$&nbsp;true. This is the case iff $\vDash \varphi\Rightarrow\psi$, i.e., if the formula $\varphi\Rightarrow\psi$ is true in all truth assignments (is a tautology).

Entailment and implication operate at different levels. An implication is something that may be true or false, depending on which truth assignment you're considering at the moment, whereas an entailment is a statement about all truth assignments.  In particular, the truth of the entailment $\varphi\vDash\psi$ depends only on truth assignments that make $\varphi$&nbsp;true. If a particular truth assigment makes $\varphi$&nbsp;false, then it cannot make the entailment false. Similarly, if an assignment makes $\varphi$&nbsp;false, it cannot make the implication $\varphi\Rightarrow\psi$ false.