Explanation Consider the following argument, p ∼ p → ∼ q q → r ∴ r Definition: An argument is a series of statement called premises followed by a single statement called the conclusion. An argument is valid if whenever all the premises are true, then the conclusion must also be true. List of valid arguments is given below, Law of Detachment Law of Contraposition Law of Syllogism Disjunctive Syllogism p → q p ∴ q p → q ∼ p ∴ ∼ q p → q q → r ∴ p → r p ∨ q ∼ p ∴ q List of some invalid argument is given below, Fallacy of the Converse Fallacy of the Inverse p → q q ∴ p p → q ∼ p ∴ ∼ q Approach: The truth table is given below, Premise 1 Premise 2 Premise 3 Conclusion p q r ∼ p ∼ q p ∼ p → ∼ q q → r r T T T

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Chapter 3.4, Problem 24E

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Whether the following argument is valid,

p ∼p→∼qq→r∴ r .

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Chapter 3.4, Problem 23E

Chapter 3.4, Problem 25E

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Whether the following argument is valid, p ∼ p → ∼ q q → r ∴ r .

Whether the following argument is valid, p ∼p→∼qq→r∴ r .

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Chapter 3 Solutions

Whether the following argument is valid,

p ∼p→∼qq→r∴ r .