<P>Problem 4 of Review Questions of Chapter 1 </P>
<P>     a) For two propositions to be logically equivalent they would have to have the same truth value no matter
what the truth values of the propositions within the compound proposition are.
<P>     b) The different ways to compound propositions can be shown to be equivalent are by using truth tables to
determine truth table equivalence, or by using known logical equivalences to step by step show the process to obtain
the other compound proposition. You can also prove they are equivalent if (p <-> q) is a tautology.
<P>     c) Two different ways to show that -p v (r -->  -q)    and  -p  v  -q  v  -r are logically equivalent:
<P>     *Truth table
        <CODE>
        P       Q       R       -p      -q      -r      r --> -q  -p v .q    -p v (r --> -q)  -p v -q v -r
        F       F       F       T       T       T       T         T          T                T
        F       F       T       T       T       F       T         T          T                T
        F       T       F       T       F       T       T         T          T                T
        F       T       T       T       F       F       F         T          T                T
        T       F       F       F       T       T       T         T          T                T
        T       F       T       F       T       F       T         T          T                T
        T       T       F       F       F       T       T         F          T                T
        T       T       T       F       F       F       F         F          F                F
        </CODE>
<P>     The truth tables are the same so they are logically equivalent
<P>     *Series of Logical equivalences
<P>     -p v ( r --> -q) = -p v ( -r v -q)  by the Table 7 on page 25 in the book
<P>     -p v -r v -q = -p v -q v -r by the Commutative law