Do you know what a half-adder is supposed to do? it takes two binary bits, and adds them together. a binary bit takes values 0 or 1, or True or False, or any two differing values.
you should be able to come up with a list of all possible inputs yourself. and if you consider adding the numbers "0" and "1" together in binary... you should be able to consider the outputs, a 'sum' value and a 'carry' value.