title: Boolean operators and Induction
body: <p>Let @ denote the binary boolean operator defined by the right-hand side below:
  p @ q = (p ^ ¬q)</p>
  
  <p>(b) Is the set of operators {@, ¬} complete? Explain in detail.</p>
  
  <p>(c) Prove by induction that any propositional formula in a single propositional variable <em>p</em> that uses only the boolean operator @ (or no operators at all) is equivalent
  to either the truth value False or to the single propositional variable <em>p</em>. Explain.</p>