No, predation is not a symbiotic relationship.
There are five different kinds of symbiotic relationships:
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Predation is an interaction between species. One of the participants acts as the "predator" and kills - and usually consumes - the other species, known as the "prey". In a symbiotic relationship, two different species live in direct contact with one another. Predation would be the interaction between two species that involves the satiation of one, at the expense of the life of the other.
Symbiotic organisms only affect their host, where as predators and prey affect their surrounding environment as well.