Who are the 7 demigods in the heros of olympus? why are they on a quest? who dies? is this a myth? is this a true story?

The 7 demigods are Jason,Piper,Frank,Hazel,Annabeth,Percy, and Leo. Leo dies in the last book Blood of Olympus. This isn't a myth or true story.  

At Camp Half-Blood, a quest can only be given if a camper receives a prophecy from the Oracle. At Camp Jupiter, the campers must also have a prophecy in order to attain a quest. However, unlike Camp Half-Blood, the prophecy is given by the Auguries by reading the stuffing of plush toys. After a prophecy is given, the matter is then brought before the Senate of New Rome to decide the details, including companions, strategy, and even what supplies will be given to the questers. Where Jason, Piper, and Leo return Jason's memory. As Frank, Percy, and Hazel try to return Percy's memory. In the Mark of Athena. Jason and Percy restore their memory and Piper,Leo, and Annabeth go to Camp Juipter then to get Percy. There they start their quest

**SPOILERS** ( You have been warned...)  

Prophecy: Seven half bloods shall answer the call,

                  To storm or fire, the world will fall,

                     An oath to keep with the final breath,

                        And foes bear arms to the doors of death.

The Seven Demigods of The Second Great Prophecy are:

Perseus (Percy) Jackson, Annabeth Chase, Leonidas (Leo) Valdez, Piper McLean, Jason Grace, Hazel Levesque, and Frank Zhang.

They go on a quest to close the doors of death, bring peace between the Greek and Romans, but overall the reason for their quest is to defeat the Goddess Gaia.

Out of the seven, Leo Valdez die in the explosion that destroyed Gaia,  but due to the Physician's Cure, Leo came back to life, and freed Calypso from her Island. This fulfilled the part of the prophecy " an oath to keep with the final breath."

This is not a myth, but based upon tales from Greek mythology. It includes characters, such as Hercules, Gaia, and The Olympians, from the myths.

No, this is not a true story. (From what mortals believe...;) )

honestly it just comes down to the