Logical equivalence
Logical equivalence Hello friends, Welcome to my blog mathstips4u. In my last post we have seen double implication or bi-conditional and its truth table. In this post we are going to learn logical equivalence and some of its examples. First we shall see what is meant by Statement Pattern. Let p, q, r, …be simple statements. Then a statement formed from these statements and one or more connectives Ʌ , V, ~, →, ↔ is called a statement pattern. e.g. (i) p Ʌ ̴q (ii) p Ʌ (p V q) (iii) p Ʌ (q ↔ r) etc. are statement patterns. Now we shall see Logical equivalence. Two statement patterns say and are said to logically equivalent if they have identical truth values in their last column of the truth tables. In that case we write ≡ or = Ex. Using truth table verify 1. ~ (p V q) ≡ ~ p Ʌ ~ q 2. ~ (p Ʌ q)...