Explanation Given Information: The given circuit is: Formula used: Distributive law: [ P ∧ ( Q ∨ R ) ] ⇔ [ ( P ∧ Q ) ∨ ( P ∧ R ) ] Negation law: ( P ∨ ~ P ) ⇔ t Identity law: ( P ∧ t ) ⇔ P Commutative law: ( P ∨ Q ) ⇔ ( Q ∨ P ) Associative law: [ ( P ∨ Q ) ∨ R ] ⇔ [ P ∨ ( Q ∨ R ) ] DeMorgan’s law: ∼ ( P ∨ Q ) ⇔ ( ∼ P ∧ ∼ Q ) Calculation: Consider the given circuit: Translate the circuit in logical symbols as below: 1. Start with the OR Gate. 2. Move back, then there are two sub gates: OR Gate and NOT Gate. 3. Simplify them individually. Thus, the circuit can be translated as the logic statement: ( ~ ( p ∨ q ) ) ∨ ( p ∨ r ) Now simplify ( ~ ( p ∨ q ) ) ∨ ( p ∨ r ) as below: Apply DeMorgan’s law, ( ~ ( p ∨ q ) ) ∨ ( p ∨ r ) ⇔ ( ~ p ∧ ~ q ) ∨ ( p ∨ r ) Apply distributive law and associative law, ( ~ ( p ∨ q )

12th Edition

ISBN: 9781323788707

Author: Goldstein

Publisher: PEARSON

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Chapter 11.7, Problem 10E

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Chapter 11.7, Problem 9E

Chapter 11.7, Problem 11E

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Chapter 11 Solutions

FINITE MATHEMATICS & ITS APPLICATIONS

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 simplified form of the circuit given below:

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Chapter 11 Solutions