EXAMPLE2 PropOSItIonal Equvalence 命题演算 Show that(pVg) and- pA g are logically equivalent. This equivalence is one of De morgan's laws for propositions, named after the English mathematician Augustus De Morgan, of the mid-nineteenth century Solution: The truth tables for these propositions are displayed in Table 2 Since the truth values of the propositions (pVg and pA q agree for all possible combinations of the truth values of p and g, it follows that these propositions are logically equivalent. 2/24/202111:14PM Deren Chen, Zhejiang UnivPropositional Equivalences 命题演算 2/24/2021 11:14 PM Deren Chen, Zhejiang Univ. 7 EXAMPLE 2 Show that (p∨q) and p∧ q are logically equivalent. This equivalence is one of De Morgan's laws for propositions, named after the English mathematician Augustus De Morgan, of the mid-nineteenth century. Solution: The truth tables for these propositions are displayed in Table 2. Since the truth values of the propositions (p∨q) and p∧ q agree for all possible combinations of the truth values of p and q, it follows that these propositions are logically equivalent.   