Explanation Given Information: The given logic statement is ( ∼ p ∨ ∼ q ) ∧ ( ∼ p ∧ r ) . The given values for variables are p = 1 , q = 0 , r = 1 . Formula Used: The NOT gate/inverter performs the function of negating the input. It has one input line with current input that is either 1 or 0. The AND gate behaves exactly as the logical connective AND ( ∧ ) . Current flows through the gate from two inputs if and only if both input currents are ON. Thus, the output is 1 if and only if both inputs are ON. The OR gate behaves exactly as the logical connective ( ∨ ) . Current flows through the OR gate if and only if at least one of the input currents is ON. Thus, the output of the OR gate is ON if and only if at least one of the inputs is ON. Calculation: The given logic statement is ( ∼ p ∨ ∼ q ) ∧ ( ∼ p ∧ r ) . Begin at the end with the logical connective ( ∧ ) means an AND gate and prepare the diagram for input from the two components ( ∼ p ∨ ∼ q ) and ( ∼ p ∧ r ) . In the component ( ∼ p ∨ ∼ q ) , the logical connective ( ∨ ) which means an OR gate and prepare the diagram for input from the two components ( ∼ p ) and ( ∼ q )

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

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 11.7, Problem 7E

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The logic circuit diagram for the given logic statement (∼p∨∼q)∧(∼p∧r) and the output when the variables has given values p=1,q=0,r=1.

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Chapter 11.7, Problem 6E

Chapter 11.7, Problem 8E

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Chapter 11 Solutions

Finite Mathematics & Its Applications (12th Edition)

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 logic circuit diagram for the given logic statement ( ∼ p ∨ ∼ q ) ∧ ( ∼ p ∧ r ) and the output when the variables has given values p = 1 , q = 0 , r = 1 .

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The logic circuit diagram for the given logic statement (∼p∨∼q)∧(∼p∧r) and the output when the variables has given values p=1,q=0,r=1.

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Chapter 11 Solutions