EXAMPLEA PropOSItIonal Equvalence 命题演 Show that the propositions pv(qar)and (pVgA(pvr) are logically equivalent. This is the distributive law of disjunction over conjunction Solution: We construct the truth table for these propositions in Table 4. Since the truth values of pV(q∧r)and(pVq)∧(p∨r) agree, these propositions are logically equivalent 2/24/202111:14PM Deren Chen Zhejiang univ 11Propositional Equivalences 命题演算 2/24/2021 11:14 PM Deren Chen, Zhejiang Univ. 11 EXAMPLE 4 Show that the propositions p∨(q∧r) and (p∨q)∧(p∨r) are logically equivalent.This is the distributive law of disjunction over conjunction. Solution: We construct the truth table for these propositions in Table 4. Since the truth values of p∨(q∧r) and (p∨q)∧(p∨r) agree, these propositions are logically equivalent