Explanation Given Information: The given logical connectives are ∧ , ∨ , ∼ , → , ↔ . The main mechanism for determining the truth values of statement forms is a truth table. Consider any simple statement p . Then p has one of the two truth values T (true) or F (false). The logical connective ( ∼ ) means negation. ∼ p (the negation of p ) is a form derived from p and has two possible values. When p has the truth value T, ∼ p has the truth value F, and vice versa. Truth table for Negation ( ∼ ) can be given by: p ∼ p T F F T The logical connective ( ∧ ) means conjunction. The statement form p ∧ q ( p and q ) is made up of two statements denoted by p and q and the connective ( ∧ ) . The statement p can have one of the truth values T or F. Similarly, q can have one of the truth values T or F. Hence, by the multiplication principle, there are four possible pairs of truth values for p and q . The conjunction of p and q , p ∧ q ( p and q ), is true if and only if both p is true and q is true. Truth table for Conjunction ( ∧ ) can be given by: p q p ∧ q T T T T F F F T F F F F The logical connective ( ∨ ) means disjunction. The statement form p ∨ q ( p and q ) is made up of two statements denoted by p and q and the connective ( ∨ ) . The statement p can have one of the truth values T or F. Similarly, q can have one of the truth values T or F. The disjunction of p and q , p ∨ q ( p or q ), is true if either p is true or q is true or both p and q are true. Truth table for Disjunction ( ∨ ) is given by: p q p ∨ q T T T T F T F T T F F F The logical connective ( → ) means conditional

Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

12th Edition

ISBN: 9780137442966

Author: Larry Goldstein, David Schneider

Publisher: PEARSON+

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 11, Problem 2FCCE

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The truth tables of the simple logical connectives ∧,∨,∼,→,↔.

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Chapter 11, Problem 1FCCE

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Chapter 11 Solutions

Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

Ch. 11.1 - Determine which of the following sentences are...Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 1–15, determine which sentences are...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - In Exercises 115, determine which sentences are...Ch. 11.1 - Prob. 8E

Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - In Exercises 115, determine which sentences are...Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - In Exercises 16 and 17, give the simple statements...Ch. 11.1 - Prob. 17E Ch. 11.1 - In Exercises 18 and 19, give the simple statements...Ch. 11.1 - In Exercises 18 and 19, give the simple statements...Ch. 11.1 - Prob. 20E Ch. 11.1 - The Smithsonian Museum of Natural History has...Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Let p denote the statement Paris is called the...Ch. 11.1 - Let p denote the statement Ozone is opaque to...Ch. 11.1 - 26. Let p denote the statement “Papyrus is the...Ch. 11.1 - 27. Let a denote the statement “Florida borders...Ch. 11.2 - Construct the truth table for (p~r)q.Ch. 11.2 - Construct the truth table for p~q.Ch. 11.2 - 3. Let p denote “May follows April,” and let q...Ch. 11.2 - In Exercises 14, show that the expressions are...Ch. 11.2 - Prob. 2E Ch. 11.2 - In Exercises 1–4, show that the expressions are...Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - In Exercises 528, construct truth tables for the...Ch. 11.2 - In Exercises 5–28, construct truth tables for the...Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - In Exercises 27–30, determine whether statement...Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Let p denote John Lennon was a member of the...Ch. 11.2 - Let m denote the statement The Magna Carta was...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.3 - 1. Let p denote the statement “A square is a...Ch. 11.3 - Prob. 2CYU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Construct a truth table for each of the statement...Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - In Exercises 2734, write the statement forms in...Ch. 11.3 - Prob. 28E Ch. 11.3 - In Exercises 27–34, write the statement forms in...Ch. 11.3 - Prob. 30E Ch. 11.3 - In Exercises 2734, write the statement forms in...Ch. 11.3 - In Exercises 27–34, write the statement forms in...Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.4 - Prob. 1CYU Ch. 11.4 - Prob. 2CYU Ch. 11.4 - Prob. 3CYU Ch. 11.4 - Prob. 1E Ch. 11.4 - 2. Show that the distributive laws hold:...Ch. 11.4 - Prob. 3E Ch. 11.4 - 4. Without using truth tables, show that . Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - 24. Negate the following statements: (a) Isaac...Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Tax Instruction The following statements can be...Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.5 - Show that the argument is valid. If goldenrod is...Ch. 11.5 - Show by indirect proof that the argument is valid....Ch. 11.5 - Prob. 1E Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - In Exercises 1–10, show that the argument is...Ch. 11.5 - Prob. 5E Ch. 11.5 - In Exercises 110, show that the argument is valid....Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Prob. 11E Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - In Exercises 11–20, test the validity of the...Ch. 11.5 - In Exercises 1120, test the validity of the...Ch. 11.5 - In Exercises 11–20, test the validity of the...Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - In Exercises 2124, use indirect proof to show that...Ch. 11.5 - Prob. 24E Ch. 11.5 - Prob. 25E Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Show that each of the arguments in Exercises 27...Ch. 11.6 - Prob. 1CYU Ch. 11.6 - Prob. 2CYU Ch. 11.6 - Prob. 3CYU Ch. 11.6 - Prob. 1E Ch. 11.6 - Prob. 2E Ch. 11.6 - 3. An alert California teacher chided “Dear Abby”...Ch. 11.6 - Prob. 4E Ch. 11.6 - 5. Let the universe be all university professors....Ch. 11.6 - Prob. 6E Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Let the universe consist of all nonnegative...Ch. 11.6 - Let the universe consist of all real numbers. Let...Ch. 11.6 - 11. Negate each statement by changing existential...Ch. 11.6 - Prob. 12E Ch. 11.6 - Prob. 13E Ch. 11.6 - Consider the universe of all subsets of the set...Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 16E Ch. 11.6 - Let the universal set be...Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 20E Ch. 11.7 - (a) Simplify the circuit shown in Fig. 9 by using...Ch. 11.7 - Prob. 1E Ch. 11.7 - 2. Write the logic statement represented by Fig....Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Prob. 5E Ch. 11.7 - Draw the logic circuit that represents each of the...Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Prob. 11E Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Prob. 15E Ch. 11.7 - Prob. 16E Ch. 11.7 - 17. Design a logic circuit that acts as an xor...Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Switch Design for a Lecture Hall In designing a...Ch. 11.7 - Prob. 21E Ch. 11.7 - Use the Wolfram |Alpha function Boolean Minimize...Ch. 11 - 1. What is a logical statement? Ch. 11 - Prob. 2FCCE Ch. 11 - Prob. 3FCCE Ch. 11 - What do we mean by logical equivalence? Explain...Ch. 11 - Prob. 5FCCE Ch. 11 - Prob. 6FCCE Ch. 11 - Prob. 7FCCE Ch. 11 - Prob. 8FCCE Ch. 11 - Prob. 9FCCE Ch. 11 - Prob. 10FCCE Ch. 11 - Prob. 11FCCE Ch. 11 - State De Morgans laws for quantified statements.Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - 18. Show that the argument is valid: If I shop for...Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - 21. Draw the logic circuit corresponding to the...Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - 25. Construct a statement equivalent to p XOR q,...Ch. 11 - Denise, Miriam, Sally, Nelson, and Bob are...

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The truth tables of the simple logical connectives ∧ , ∨ , ∼ , → , ↔ .

Solution Summary: The author explains that the main mechanism for determining the truth values of statement forms is a truth table.

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Chapter 11 Solutions