"The colors and symbols are important."
Translation:Los colores y símbolos son importantes.
This whole thread just became so confusing with all the senseless argument that it's difficult to keep track, I'll try to give you a clearer answer.
The answer you are looking for is it depends on context, normally when you have two or more nouns each and every one of them should have their own determiner, so under that rule, saying "los colores y símbolos son.." would be wrong, but, as always, there are exceptions. There is the possibility of having two or more nouns with only one determiner, the determiner must always match in gender and number with the closest noun.
When two or more nouns refer to the same thing or person. For example:
- Hay varias formas de preparar el biberón o tetero (Both biberón and tetero refer to a feeding bottle).
- Él es mi hermano y agente (His brother and agent are the same person).
When there is an adjective right after the determiner that modifies all the nouns. For example:
- Yo hago mi propio desayuno y almuerzo.
When the nouns are parts of only one thing, or partial aspects of a whole. For example:
- Es un premio en mérito a tu empeño y dedicación (Both empeño and dedicación are aspects of you).
- Las puertas y ventanas estaban cerradas (Both puertas and ventanas are parts of a house or a building).
Based on this exception, let's say you're doing graffiti for a gang (bad example, I know, but it's the only one I can think of), the colours are important, but also their distinctive symbols, so if you consider both nouns as aspects of that graffiti, then it is correct to say "Los colores y símbolos son importantes". I hope that clears your doubts.