A false cognate is a word that looks and/or sounds similar to a word in another language, but has a different meaning. For example, the English word "embarrassed" is a false cognate of the Spanish word "embarazada", which means "pregnant."
"Support" is a word that has very similar cognates in many languages, including:
* French: "soutien"
* Spanish: "soporte"
* German: "Support"
* Italian: "supporto"
These words all have similar meanings related to providing assistance or holding something up.
Therefore, "support" is not a false cognate. It is a word that has evolved from a common ancestor and has retained a similar meaning across languages.