Typically, $$\longrightarrow$$ is the connective used with (1); Typically, $$\wedge$$ is the connective used with (2).

(1) Universal Quantifier; (2) Existential Quantifier

(1) Existential Quantifier; (2) Universal Quantifier

A direct proof shows that the statement $$p\ \longrightarrow\ q$$ is true by...

Assuming p is true and using various rules and logical equivalences to show that q is also true

Using an example to disprove the statement

Assume p and NOT q are true and using various rules and logical equivalences to show that C AND not C exist

Assume NOT q is true and using various rules and logical equivalences to show that NOT p is also true

A proof by contraposition shows that the statement $$p\ \longrightarrow\ q$$ is true by...

Assume NOT q is true and using various rules and logical equivalences to show that NOT p is also true

Using an example to disprove the statement

Assume p and NOT q are true and using various rules and logical equivalences to show that C AND not C exist

Assuming p is true and using various rules and logical equivalences to show that q is also true

A proof by contradiction shows that the statement $$p\ \longrightarrow\ q$$ is true by...

Assume p and NOT q are true and using various rules and logical equivalences to show that C AND not C exist

Using an example to disprove the statement

Assume NOT q is true and using various rules and logical equivalences to show that NOT p is also true

Assuming p is true and using various rules and logical equivalences to show that q is also true

A proof by counterexample shows that the statement is false by...

Using an example to disprove the statement

Assume p and NOT q are true and using various rules and logical equivalences to show that C AND not C exist

Assume NOT q is true and using various rules and logical equivalences to show that NOT p is also true

Assuming p is true and using various rules and logical equivalences to show that q is also true

For the inductive step, what two parts are required?

1. IH: Assume P(k) is true for arbitrary k

1. IH: Assume P(k+1) is true for arbitrary k

CS2311 Exam 3 Review

Authored by Mary Galbraith

Computers

University

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MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Logic is built of these two parts...

Language and Rules

Syntax and Semantics

Atoms and Variables

MULTIPLE CHOICE QUESTION

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A proposition that is always true is...

Contradiction

Tautology

Contingency

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A proposition that is always false is...

Contradiction

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MULTIPLE CHOICE QUESTION

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A proposition that is sometimes false and sometimes true is...

Contradiction

Tautology

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MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Tautology

Contradiction

Contingency

None

MULTIPLE CHOICE QUESTION

10 sec • 1 pt

Tautology

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Contingency

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

Contingency

Tautology

Contradiction

None

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