Figure Out "Who Ate the Pizza?" and Explain the Answer

Essay

Figure out "Who ate the Pizza?" and explain the answer.
The Puzzle: Five roommates, Abe, Bob, Carl, Dave, and Ziggy, share an off-campus apartment. On Monday night they had leftover pizza and so they put it in the refrigerator. On Tuesday when Ziggy went to get some of that pizza he found that it had all been eaten. Later Ziggy confronted his four roommates to find out who ate the pizza. Each roommate made one statement. The person who ate the pizza lied; his statement is false. The other three statements are true. Which one ate the pizza? Here are their four statements:
Abe: I was in class all day.
Bob: Carl ate the pizza.
Carl: Bob's statement is false.
David: Carl's statement is true.