1. The Subjunctive with Doubt, Disbelief or Denial 13.2

2. 13.2 Subjunctive with verbs of doubt or denial
Whenever a sentence express doubt or denial in the main clause, the subjunctive will be used the subordinate clause because it implies uncertainty.
However, if a sentence express certainty in the main clause, the indicative will also be used in the subordinate clause
Doubt / Denial = Subjunctive
No es cierto que vengan muchas personas a la fiesta
Certainty = Indicative
Es cierto que vienen muchas personas a la fiesta.

3. Expressions of doubt *Dudar To doubt *Negar (e-ie) To deny
*No creer / pensar
To not believe / think
*No estar seguro/a de
To not be sure
*No es cierto
To not be certain
*No es verdad
To not be true
*No es obvio
It is obvious
Es (im)posible
To be (im)possible
Es (im)probable
To be (im)probable

4. Important notice
The following verbs in their opposite form represent certainty and are followed by the indicative:
SUBJUNCTIVE
INDICATIVE
*Dudar
No dudar
*Negar (e-ie)
No negar (e-ie)
*No creer
Creer
*No estar seguro/a de
Estar seguro/a de
*No es cierto
Es cierto que
*No es verdad
Es verdad que

5. Wrap your mind around it
If you think or believe it is certain, so
PENSAR and CREER in the affirmative form are followed by the Indicative.
Pienso que es una buena idea ir al cine el Viernes.
Expressions involving possibility or probability are always uncertain, so
(No) es (im)posible and (No) es (im)probable are followed by the Subjunctive.
Es imposible que yo reciba un coche de Navidad.