We don't have any synonyms for give encouragement yet.
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Definition of give encouragement:
(n) :
the act of encouraging; incitement to action or to practice; as, the encouragement of youth in generosity; that which serves to incite, support, promote, or advance, as favor, countenance, reward, etc.; incentive; increase of confidence; as, the fine arts find little encouragement among a rude people
"all generous encouragement of arts. -Otway."