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8. True or False? Use your knowledge of natural deduction in propositional logic, and your knowledge of the rules of replacement, to determine which of the following statements are true. Check all that apply. According to the material implication rule (Impl), p:: (p v p). O Transposition (Trans) is the only rule you have that directly applies to biconditional statements. O ND• ND is logically equivalent to D. The expression (B• G) V (~B • NG) is logically equivalent to the expression B = G. Rules of replacement are applicable only to whole lines in a proof. Rules of replacement are "one-way" rules. Rules of replacement are not rules of implication. Rules of implication are expressed by pairs of logically equivalent statement forms. The expression A B is logically equivalent to the expression ~B ɔ NA. The axiom of replacement asserts that, within a proof, logically equivalent expressions may replace each other. O O O O OO O O

8. True or False? Use your knowledge of natural deduction in propositional logic, and your knowledge of the rules of replacement, to determine which of the following statements are true. Check all that apply. According to the material implication rule (Impl), p:: (p v p). O Transposition (Trans) is the only rule you have that directly applies to biconditional statements. O ND• ND is logically equivalent to D. The expression (B• G) V (~B • NG) is logically equivalent to the expression B = G. Rules of replacement are applicable only to whole lines in a proof. Rules of replacement are "one-way" rules. Rules of replacement are not rules of implication. Rules of implication are expressed by pairs of logically equivalent statement forms. The expression A B is logically equivalent to the expression ~B ɔ NA. The axiom of replacement asserts that, within a proof, logically equivalent expressions may replace each other. O O O O OO O O

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. True or False? Use your knowledge of natural deduction in propositional logic, and your knowledge of the rules of replacement, to determine which of the following statements are true. Check all that apply. O According to the material implication rule (Impl), p :: (p v p). O Transposition (Trans) is the only rule you have that directly applies to biconditional statements. ND• ND is logically equivalent to ~D. O The expression (B • G) V (~B• G) is logically equivalent to the expression B = G. Rules of replacement are applicable only to whole lines in a proof. O Rules of replacement are "one-way" rules. Rules of replacement are not rules of implication. Rules of implication are expressed by pairs of logically equivalent statement forms. O The expression A ɔ B is logically equivalent to the expression -B ɔ NA. O The axiom of replacement asserts that, within a proof, logically equivalent expressions may replace each other. O O
Transcribed Image Text:8. True or False? Use your knowledge of natural deduction in propositional logic, and your knowledge of the rules of replacement, to determine which of the following statements are true. Check all that apply. O According to the material implication rule (Impl), p :: (p v p). O Transposition (Trans) is the only rule you have that directly applies to biconditional statements. ND• ND is logically equivalent to ~D. O The expression (B • G) V (~B• G) is logically equivalent to the expression B = G. Rules of replacement are applicable only to whole lines in a proof. O Rules of replacement are "one-way" rules. Rules of replacement are not rules of implication. Rules of implication are expressed by pairs of logically equivalent statement forms. O The expression A ɔ B is logically equivalent to the expression -B ɔ NA. O The axiom of replacement asserts that, within a proof, logically equivalent expressions may replace each other. O O
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