Per post #2, draw up a truth table. Think about a multiplexer and how to make the output agree with the truth table. A full adder requires a carry bit - can a MUX do that by itself?
Build up to it with a half adder. make the truth table using A & B as the two bits, X as the output. Look at a MUX and see if you can't get A & B to select the X value in the truth table for the multiplexer's output.