Entailment \(A \vDash B\)

• In all the models that \(A\) is true, \(B\) must also be true
• \(F \vDash T\) is true
• \(A\) has a smaller "truth space" than \(B\)
• Examples
  \(\alpha \wedge \beta \vDash \alpha\)
  \(\alpha \vDash \alpha \vee \beta\)
  \(\alpha \vDash (\beta \vee \gamma) \Longrightarrow (\alpha \vDash \beta \vee \alpha \vDash \gamma)\) is not true;
  Counterexample: \(\beta = \alpha, \gamma = \neg\alpha\)