Consider a set of logic functions $$\{ f_1(A), f_2(A), f_3(A), f_4(A)\}$$ that take a proposition ($$A$$) as input which is either True or False. These functions map the truth value of the input proposition to either True or False according to some unknown rules. We want to discover these rules. Given the following truth table, we want to show that,

necessitates the equivalence of our four logic functions with the following logical operators. To do so, you can draw the truth table corresponding to these logical operations to show that they have same values as their corresponding logic functions in the truth table in the above.