True or false: If $T\vDash (p\lor q)$, then either $T\vDash p$ or $T\vDash q$.

Question

True or False.
For any set of sentences, T, if T semantically entails (double turnstile symbol) p v q, then either T semantically entails p or T semantically entails q.

Answer 1

False.

$\{(p\vee q)\}\models(p\vee q)$ but $\{(p\vee q)\}\not\models p$ and $\{(p\vee q)\}\not\models q$ .