Determine the contrapositive of each of the following statements.

$($a$)$ If John is an artist, then he is poor.

$($b$)$ Only if Mary studies will she pass the test.

Prove the following argument is valid:

$pq$

$rq$

:$.rp$

Write the the input$/$output truth table for the following two circuits shown in Figure $1$ and Figure

In both figures, $A,B($and $C)$ are inputs and $x$ is output.