Chapter 1: Logic

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Chapter 1: Logic

1.1 Propositions and logical operations

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Different ways to express a conjunction in English

The disjunction operation

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Ambiguity of “or” in English

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1.1.2: Propositions and logical operations.

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1.2 Evaluating compound propositions

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Example 1.2.1: Searching the web.

Filling in the rows of a truth table

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Example 1.2.2: Logic in electronic devices.

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1.2.3: Truth values for compound propositions.

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1.2.4: Writing truth tables.

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1.2.5: Translating compound propositions into English sentences.

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1.3 Conditional statements

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The converse, contrapositive, and inverse

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The biconditional operation

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Compound propositions with conditional and biconditional operations

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Example 1.3.1: Automatic degree requirements check.

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1.4 Logical equivalence

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De Morgan’s laws

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1.5 Laws of propositional logic

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Using the laws of propositional logic to show logical equivalence

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De Morgan’s law

Conditional identity

Double negation law

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1.5.3: Expand then reduce the proposition.

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Distributive

Commutative

De Morgan’s

Conditional

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1.6 Predicates and quantifiers

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Universal quantifier

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Existential quantifier

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1.7 Quantified statements

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Translating between English statements and quantified statements

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1.7.4: Quantified statements in logic and English.

Example 1.7.1: Translating quantified statements from English to logic.

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1.8 De Morgan’s law for quantified statements

De Morgan’s law for quantified statements

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1.9 Nested quantifiers

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Nested quantifiers of the same type

Alternating nested quantifiers

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De Morgan’s law with nested quantifiers

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1.10 More nested quantified statements

Using logic to express “everyone else”

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Expressing uniqueness in quantified statements

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Moving quantifiers in logical statements

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1.11 Logical reasoning

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1.12 Rules of inference with propositions

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1.13 Rules of inference with quantifiers

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is an arbitrary element of the domain

Multiple uses of existential instantiation: a common mistake

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Showing an argument with quantified statements is invalid

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