What genre of dance music with roots in swing jazz and blues singing was popular from the late 1940s through the early 60s, and evolved into a tradition that continues today?

It is the genre of Rhythm and blues (R&B).

Explanation:

It is known as music to art that is characterized by rhythms, sounds, melody, and harmony, which is heard by people in different situations. Music is an important cultural element for people because, through them, they can express their feelings and opinions.

In music different types are characterized among them Rhythm and Blues (R&B). The rhythm and blues had its origins in the United States, it is a genre of famous African-American music that has roots in jazz and blues music. The rhythm and blues music is characterized by having a lively and urban rhythm.  

Currently, R&B is confused with the Trap genre, since both have similar electronic sounds. The principal R&B singers are Craig David, Destiny´s Child, Tina Turner, Alicia Keys, among others.

I hope this information can help you.

the answer might be either a or c. can't be too sure , because i searched the web, but no valid answers came through.