Chapter 7.1, Problem 2ED

If a compound proposition contains three variables $p,q,\text{ and }r\text{,}$ then its truth table will have eight rows, one for each of the eight ways of assigning truth values to $p,q,\text{ and }r\left(\text{TTT,TTF,TFT,TFF,FTT,FTF,FFT,FFF}\right)$. Construct truth tables to verify the following logical implications and equivalences:

$\begin{array}{l}\left(\text{A}\right)\left(p\to q\right)\wedge \left(q\to r\right)\Rightarrow \left(p\to r\right)\\ \\ \left(\text{B}\right)p\wedge \left(q\vee r\right)\equiv \left(p\wedge q\right)\vee \left(p\vee r\right)\\ \\ \left(\text{C}\right)p\vee \left(q\wedge r\right)\equiv \left(p\vee q\right)\wedge \left(p\vee r\right)\end{array}$