(Solved): Write the statement in symbolic form using the symbols \( \sim, \vee \), and \( \wedge \) and the ...

Write the statement in symbolic form using the symbols \( \sim, \vee \), and \( \wedge \) and the indicated letters to represent component statements. Let \( p=" x>4, " q=" x=4 \)," and \( r=" 12>x . " \) (a) \( x \geq 4 \) \[ \begin{array}{l} p \sim q \\ p \wedge q \\ p \vee q \\ p \vee r \\ q \sim r \end{array} \] (b) \[ \begin{aligned} 12> & >4 \\ r & \sim p \\ p & \sim q \\ r & \wedge p \\ & p \wedge q \\ & r \vee p \end{aligned} \] (c) \[ \begin{aligned} 12> & x \geq 4 \\ & r \vee(p \wedge q) \\ & r \wedge(p \vee q) \\ & p \wedge(q \vee r) \\ & r \sim(p \vee q) \\ & r \wedge(p \sim q) \end{aligned} \]