(Solved): Construct a truth table for the given statement. \[ \sim \mathrm{n} \rightarrow \sim \mathrm{m} \] ...

Construct a truth table for the given statement. \[ \sim \mathrm{n} \rightarrow \sim \mathrm{m} \] Fill in the truth table. Construct a truth table for the given statement. \[ (\sim p \rightarrow q) \leftrightarrow(\sim p \wedge q) \] Fill in the truth table. Show that \( (\sim \mathrm{x} \rightarrow \sim \mathrm{y}) \Leftrightarrow(\sim \mathrm{y} v \mathrm{x}) \). First, construct a truth table for the statement \( (\sim x \rightarrow \sim y) \). Complete the table below. Show that \( b \rightarrow a \) is logically equivalent to \( \sim(b \wedge \sim a) \). Construct a truth table for \( \mathrm{b} \rightarrow \mathrm{a} \).