Every compound statement is equivalent to a statement using only the connectives of conjunction and negation. To see this, we need to find equivalent wffs for \(A \vee B\) and for \(A \rightarrow B\) that use only \(\wedge\) and '. These new statements can replace, respectively, any occurrences of \(A \vee B\) and \(A \rightarrow B\). (The connective \(\leftrightarrow\) was defined in terms of other connectives, so we already know that it can be replaced by a statement using these other connectives.)

a. Show that \(A \vee B\) is equivalent to \(\left(A^{\prime} \wedge B^{\prime}\right)^{\prime}\)

b. Show that \(A \rightarrow B\) is equivalent to \(\left(A \wedge B^{\prime}\right)^{\prime}\)

Exercises 47-50 show that defining four basic logical connectives (conjunction, disjunction, implication, and negation) is a convenience rather than a necessity because certain pairs of connectives are enough to express any wff.