Explanation The disjunction is true if at least one of the components of the disjunction is true. The disjunction is false if both the statements are false. The conjunction is true if both the components of the conjunction is true. The conjunction is false if at least one of the statements is false. If the statement p is true, the conditional statement will depend on whether the statement q is true or false. If the statement p is false, the conditional statement will be true and does not depend on whether the statement q is true or false. The negation ∼ p is the opposite of the statement p . If the component of the statement is true, the negation of statement is false and vice-versa. An argument having n premises P 1 , P 2 , P 3 , ... , P n and conclusion C can be represented by the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C . An argument is valid if and only if the conditional [ P 1 ∧ P 2 ∧ P 3 ∧ ... ∧ P n ] → C is a tautology. Approach: Consider the argument p → q q ∧ r ∴ p ∨ r . Therefore, the conditional for the argument is, [ ( p → q ) ∧ ( q ∧ r ) ] → ( p ∨ r ) There are 3 letters in the given symbolic expression. So, there will be 2 3 = 8 rows in the truth table

11th Edition

ISBN: 9781337496094

Author: Tan

Publisher: CENGAGE C

See similar textbooks

Concept explainers

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities.…

Videos

Question

Chapter A.5, Problem 6E

To determine

To check:

The validity of the argument p→qq∧r∴p∨r.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter A.5, Problem 5E

Chapter A.5, Problem 7E

Students have asked these similar questions

①(a) Let rεR, o≤r<1. Prove directly from defintions. 2 = r ++²+3+... that the series r = 1 is convergent with sum 1-2 +p+.... (b) Prove that the harmonic series 2 ½ is divergent. นะเ n ② (a) Define what is meant by the following: (1) the sequence (an) is convergent. (ii) the sequence (an) is Cauchy. (ii) the sequence (an) is bounded. (b) Prove directly from definitions that a Cauchy Sequence is bounded. ③ (a) Prove diredly from definitions that if a Cauchy Sequence (an) has a convergent subsequence then (an) is convergent. (6) Use the results of 2(b) and 3(a) to deduce that a Counchy sequence is convergent. You may assume the Bolzano- Weierstrass Theorem.

Producers' Surplus A supplier of portable hair dryers will make x hundred units of hair dryers available in the market when the unit price is P169+ 4x dollars. Determine the producers' surplus if the market price is set at $17/unit. (Round your answer to two decimal places.) $50547.33

Express the solution of the given initial value problem as a sum of two oscillations. Primes denote derivatives with respect to time t. Graph the solution function x(t) in such a way that you can identify and label its period. x" + 49x=26 cos 6t; x(0) = x'(0) = 0

Chapter A Solutions

FINITE MATH.F/MGRL....(LL)>CUSTOM PKG.<

Ch. A.1 - In Exercises 114, determine whether the statement...Ch. A.1 - Prob. 2E Ch. A.1 - Prob. 3E Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E

Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Prob. 14E Ch. A.1 - Prob. 15E Ch. A.1 - Prob. 16E Ch. A.1 - Prob. 17E Ch. A.1 - Prob. 18E Ch. A.1 - Prob. 19E Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Let p and q denote the propositions p: The...Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.1 - Prob. 33E Ch. A.2 - Prob. 1E Ch. A.2 - Prob. 2E Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - In Exercises 1-18, construct a truth table for...Ch. A.2 - Prob. 9E Ch. A.2 - Prob. 10E Ch. A.2 - Prob. 11E Ch. A.2 - Prob. 12E Ch. A.2 - Prob. 13E Ch. A.2 - Prob. 14E Ch. A.2 - Prob. 15E Ch. A.2 - Prob. 16E Ch. A.2 - Prob. 17E Ch. A.2 - Prob. 18E Ch. A.2 - If a compound proposition consists of the prime...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - In Exercises 14, write the converse, the...Ch. A.3 - Prob. 3E Ch. A.3 - Prob. 4E Ch. A.3 - Prob. 5E Ch. A.3 - In Exercises 5 and 6, refer to the following...Ch. A.3 - Prob. 7E Ch. A.3 - Prob. 8E Ch. A.3 - Prob. 9E Ch. A.3 - Prob. 10E Ch. A.3 - Prob. 11E Ch. A.3 - Prob. 12E Ch. A.3 - Prob. 13E Ch. A.3 - Prob. 14E Ch. A.3 - Prob. 15E Ch. A.3 - Prob. 16E Ch. A.3 - Prob. 17E Ch. A.3 - Prob. 18E Ch. A.3 - Prob. 19E Ch. A.3 - Prob. 20E Ch. A.3 - Prob. 21E Ch. A.3 - Prob. 22E Ch. A.3 - Prob. 23E Ch. A.3 - Prob. 24E Ch. A.3 - Prob. 25E Ch. A.3 - Prob. 26E Ch. A.3 - Prob. 27E Ch. A.3 - Prob. 28E Ch. A.3 - Prob. 29E Ch. A.3 - Prob. 30E Ch. A.3 - Prob. 31E Ch. A.3 - Prob. 32E Ch. A.3 - Prob. 33E Ch. A.3 - Prob. 34E Ch. A.3 - Prob. 35E Ch. A.3 - Prob. 36E Ch. A.3 - Prob. 37E Ch. A.3 - Prob. 38E Ch. A.4 - Prove the idempotent law for conjunction, ppp.Ch. A.4 - Prob. 2E Ch. A.4 - Prove the associative law for conjunction,...Ch. A.4 - Prob. 4E Ch. A.4 - Prove the commutative law for conjunction, pqqp.Ch. A.4 - Prob. 6E Ch. A.4 - Prob. 7E Ch. A.4 - Prob. 8E Ch. A.4 - Prob. 9E Ch. A.4 - Prob. 10E Ch. A.4 - Prob. 11E Ch. A.4 - Prob. 12E Ch. A.4 - Prob. 13E Ch. A.4 - Prob. 14E Ch. A.4 - Prob. 15E Ch. A.4 - Prob. 16E Ch. A.4 - Prob. 17E Ch. A.4 - In exercises 9-18, determine whether the statement...Ch. A.4 - Prob. 19E Ch. A.4 - Prob. 20E Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 22E Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - In Exercises 21-26, use the laws of logic to prove...Ch. A.4 - Prob. 26E Ch. A.5 - Prob. 1E Ch. A.5 - Prob. 2E Ch. A.5 - Prob. 3E Ch. A.5 - Prob. 4E Ch. A.5 - Prob. 5E Ch. A.5 - Prob. 6E Ch. A.5 - Prob. 7E Ch. A.5 - Prob. 8E Ch. A.5 - Prob. 9E Ch. A.5 - In Exercises 116, determine whether the argument...Ch. A.5 - Prob. 11E Ch. A.5 - Prob. 12E Ch. A.5 - Prob. 13E Ch. A.5 - Prob. 14E Ch. A.5 - Prob. 15E Ch. A.5 - Prob. 16E Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 18E Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - In Exercises 17-22, represent the argument...Ch. A.5 - Prob. 22E Ch. A.5 - Prob. 23E Ch. A.5 - Prob. 24E Ch. A.5 - Prob. 25E Ch. A.6 - In Exercises 1-5, find a logic statement...Ch. A.6 - Prob. 2E Ch. A.6 - Prob. 3E Ch. A.6 - Prob. 4E Ch. A.6 - Prob. 5E Ch. A.6 - Prob. 6E Ch. A.6 - Prob. 7E Ch. A.6 - Prob. 8E Ch. A.6 - Prob. 9E Ch. A.6 - Prob. 10E Ch. A.6 - Prob. 11E Ch. A.6 - Prob. 12E Ch. A.6 - Prob. 13E Ch. A.6 - In Exercise 12-15, find a logic statement...Ch. A.6 - Prob. 15E Ch. A.6 - Prob. 16E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To check: The validity of the argument p → q q ∧ r ∴ p ∨ r .

Solution Summary: The author evaluates the validity of the argument lpto q

Concept explainers

Videos

To check:

The validity of the argument p→qq∧r∴p∨r.

Want to see the full answer?

Chapter A Solutions

To check: The validity of the argument p → q q ∧ r ∴ p ∨ r .

Solution Summary: The author evaluates the validity of the argument lpto q

Concept explainers

Videos

To check: The validity of the argument p→qq∧r∴p∨r.

Want to see the full answer?

Chapter A Solutions

To check:

The validity of the argument p→qq∧r∴p∨r.