Question 6: In this exercise, we will denote Boolean variables by lowercase letters, such as p and q. A proposition is any Boolean formula that can be obtained by applying the following recursive rules 1. For every Boolean variable p, p is a proposition. 2. If f is a proposition, then is also a proposition. 3. If f and g are propositions, then (f V g) is also a proposition 4. If f and g are propositions, then (f g) is also a proposition . Let p and q be Boolean variables. Prove that is a proposition Let t denote the not-and operator. In other words, if f and g are Boolean formulas then (f t g is the Boolean formula that has the following truth table (0 stands for false, and 1 stands for true) 0 Let p be a Boolean variable. Use a truth table to prove that the Boolean formulas (pt p) and-p are equivalent Let p and q be Boolean variables. Use a truth table to prove that the Boolean formulas ((p tp) t ( and p V q are equivalent. Let p and q be Boolean variables. Express the Boolean formula (p A q) as an equivalent Boolean formula that only uses the -operator. Use a truth table to justify your answer. . Prove that any proposition can be written as an equivalent Boolean formula that only uses the 1-operator