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Propositions: A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both. EXAMPLE 1 All the following declarative sentences are propositions. Washington, D.C., is the capital of the United States of America. Toronto is the capital of Canada. 1 + 1 = 2. 2 + 2 = 3.
Exercise Sheet 1: Propositional Logic 1. Let p stand for the proposition“I bought a lottery ticket”and q for“I won the jackpot”. Express the following as natural English sentences: (a) ¬p (b) p∨ q (c) p∧ q (d) p ⇒ q (e) ¬p ⇒¬q (f) ¬p∨ (p∧ q) 2. Formalise the following in terms of atomic propositions r, b, and w, first ...
proposition is a declarative sentence that is either true or false. Examples of propositions: The Moon is made of green cheese. Trenton is the capital of New Jersey. Toronto is the capital of Canada. 0 + 0 = 2 Examples that are not propositions. Sit down! What time is it?
This le contains an English version of exercises in the course of Discrete mathematics. Most of the problems were prepared by Michael Kubesa, Tereza Kova rov a, and Petr Kov a r.
EXAMPLE 1 : We can construct examples of tautologies and contradictions using just one propositional variable. Consider the truth tables of p ∨¬p and p ∧¬p, shown in Table 1. Because p ∨¬p is always true, it is a tautology. Because p ∧¬p is always false, it is a contradiction.
This document contains practice problems related to propositional logic and predicate logic. It defines several propositions and predicates, and asks the reader to symbolize statements using those definitions, construct truth tables, and translate between logical expressions and English sentences.
Discrete Mathematics (Propositional Logic) Pramod Ganapathi DepartmentofComputerScience StateUniversityofNewYorkatStonyBrook January31,2021
