Final answer:
The person would have lied if they promised to give a million dollars when they did not win the lottery.
Step-by-step explanation:
To determine if someone lied about winning a lottery and promising to give someone a million dollars, we need to evaluate the truth values of the statements involved. Let p represent the statement 'I win a lottery' and q represent the statement 'I give you a million dollars.' The promise made by the person is 'if I win a lottery I will give you a million dollars,' which can be represented as p → q.
If the person did not win a lottery (¬p), then the promise would not be fulfilled and they would have lied. However, if the person did win a lottery and gave the million dollars (p → q is true), then they did not lie. So, the only case where they would have lied is if they promised to give a million dollars when they did not win the lottery.