Sam Giancana, a famous mafia boss in Chicago, had an extensive relationship with the Kennedy family. He was business partners with JFK's father, Joseph, and later helped the family gain political power. Joseph Kennedy had a close relationship with Sam Giancana during Prohibition because they were bootleggers together. Later in 1960, Joseph Kennedy asked Giancana for help in securing enough votes for JFK's presidential election. It is speculated that JFK won the state of Illinois, and therefore the election, because of Sam Giancana's influence in Chicago. Despite helping him win the election, JFK still appointed Robert Kennedy to Attorney General knowing his plans to minimize organized crime. This did not please the mafia and could have been enough of a reason to assassinate Kennedy.
There is no proof that Sam Giancana or the mafia was involved with the JFK assassination. Many link Giancana to the investigation because of his anger toward Robert Kennedy's moves against the mob, but there has been no evidence or investigation into this theory. Giancana never testified on the Kennedy assassination, nor was he suspected of being involved. Therefore, there is no evidence that the mafia was behind JFK's assassination.
[P1] Sam Giancana had ties to the Kennedy family. [P2] Sam Giancana helped JFK win the presidential election. [P3] The mafia was angry about Robert Kennedy's moves against organized crime. [P4] Therefore, the mafia assassinated JFK.
Rejecting the premises
[Rejecting P4] There's no proof that this is the case.