(a) Explanation Given information: The logical implication p ⇒ [ q → ( p ∧ q ) ] . Formula used: Let P and Q be two statement forms. The logical implication P ⇒ Q holds if the implication statement P → Q is a tautology. Proof: Let the statements p and [ q → ( p ∧ q ) ] be represented as P and Q respectively. The logical implication P ⇒ Q can be proved if the implication statement P → Q is proven to be a tautology. The implication statement P → Q can be written as p → [ q → ( p ∧ q ) ] . Consider the truth table for logical statements p ∧ q and p → q , p q p → q p ∧ q T T T T T F F F F T T F F F T F (b) To determine Whether the logical equivalence statement, p ⇔ [ q → ( p ∧ q ) ] is true or false.

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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Chapter 11.4, Problem 6E

(a)

To determine

To prove: The logical implication statement, p⇒[q→(p∧q)] holds.

(b)

To determine

Whether the logical equivalence statement, p⇔[q→(p∧q)] is true or false.

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Chapter 11.4, Problem 5E

Chapter 11.4, Problem 7E

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. 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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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To prove: The logical implication statement, p ⇒ [ q → ( p ∧ q ) ] holds.

Solution Summary: The author explains how the logical implication statement pRightarrow left holds if the statement is a tautology.