Complete the following truth table.

Determine whether the compound proposition $\neg \left( {(r \wedge p) \vee \neg q)} \right) \Leftrightarrow \neg (r \wedge p) \wedge q$ is a tautology, a contradiction or neither.

Give a reason.

    (A1)(A1)(ft)(A1)(ft)(A1)     (C4)

Notes: Award (A1) for each correct column.

For the “${(r \wedge p) \vee \neg q}$” follow through from the “$r \wedge p$” column.

For the “$\neg \left( {(r \wedge p) \vee \neg q)} \right)$” column, follow through from the preceding column.

tautology     (A1)(ft)

columns $\neg \left( {(r \wedge p) \vee \neg q)} \right)$ and $\neg (r \wedge p) \wedge q$ are identical     (R1)(C2)

Notes: Do not award (R0)(A1)(ft). Follow through from their table in part (a).

Award the (R1) for an additional column representing $\neg \left( {(r \wedge p) \vee \neg q)} \right) \Leftrightarrow \neg (r \wedge p) \wedge q$ that is consistent with their table.