Propositional logic examples pdf

Throughout our study of discrete mathematics, we will be given propositional statements that form an argument as we will then need to decide whether the given argument is valid or not. We will extract symbols and perform calculations, just like we would in algebra, and ultimately reach a conclusion based on our results. What is extremely important to emphasize and point out is that the negation of a statement will always have the opposite truth value compared with the original statement.

With compound statements, the ability to determine its truth value can be a little more complicated. The 2-n rule says that if we have n number of unique variables, then the number of rows in the table will be 2 to the nth power. For example, if we have two individual variables, then there will be four rows because 2 to the second power is 4, and if there are three unique variables, then there will be eight rows because 2 to the 3rd power is 8.

Now the lexicographic ordering is a pattern that helps us to put values in order to make it easier to compare. Assume you have a fair coin, and you flip it twice. This means that you can get the following results:. Therefore, we must account for all possible scenarios when we construct our tables to help keep our options straight and organized so we never forget anything — we follow this simple pattern.

Therefore, our truth table must account for all possible scenarios. Throughout this lesson, we will learn how to identify propositional statements, negate propositions, understand the difference between the inclusive or and the exclusive or, translate propositions from English into symbolic logic and vise-versa, and construct truth tables for various scenarios and begin to develop the idea of logical equivalence.

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Click here to sign up. Download Free PDF. Israa Ali. A short summary of this paper. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

This is the meaning of disjunction. This is the meaning of Exclusive Or Xor. Something similar holds for the professor. This corresponds to the case where p is true and q is false. Solution: 2n We will see how to do this in Chapter 6. Section 1. When p is false and q is true all three statements are true. Solution: Let p and q be the statements that A is a knight and B is a knight, respectively. Since knights tell the truth, q must also be true.

This is called the Knowledge Base KB. Electrical System Diagram op1onal Outside Power s1 cb1 Have lights l1, l2 , wires w1 w0, w1, w2, w3, w4 , w3 switches s1, s2, s3 , and w2 circuit breakers cb1 s2 The next page gives the s3 knowledge base describing the circuit and the current w0 w4 observations. These atoms are called assumables.