The binary connective \(\downarrow\) is called the Peirce arrow, named for American philosopher Charles Peirce (not for the antique automobile). The truth table for \(\downarrow\) is given here. In Chapter 8 we will see that this truth table represents the NOR gate

Show that every compound statement is equivalent to a statement using only the connective \(\downarrow\).

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A BAB T TF F T FF T ATTF FFFT