MACM 101 Chapter Notes - Chapter 2.2: Logical Equivalence, 2Wo, Asparagine
15 Mar 2016
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Our study of logic is often referred to as the algebra of propositions. We use the truth tables of the statements or propositions to develop an idea of when two such entities are essentially the same. Example: for the primitive statements p and q, the following table will provide the truth tables for the compound statements p v q and p -> q. We will see that the two statements are exactly the same. Two statements s1, s2 are said to be logically equivalent, and we write s1 <=> s2, when the statement s1 is true (respectively, false) if and only if s2 is true (respectively, false). When s1 <=> s2 the two statements prive the same truth tables. This becomes a powerful tool to eliminate the -> and connectives from compound statements. With the connectives ^ and v we can eliminate the exclusive or (xor).
