Something is missing from the question. It should say
"Joseph Smith founded the Church of Jesus Christ of Latter Day Saints."
Assuming this is a TRUE/FALSE question, the answer is TRUE, although the church he founded was not immediately known by that name. Basically, he founded and led the movement of Mormonism, which led to the establishment of a church that eventually took the name Church of Jesus Christ of Latter Day Saints, more commonly known as the Mormon church.