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Unformatted text preview: b. ∃ x in R such that (x 2 + 2x + 1( < 0 and x = 1 c. ∀ computer science student x, is is not a math major. 4. Let R = rain F = foggy S = Sailing Race L = Lifesaving Demo T = Trophy The argument can be written as (~R ∨ ~F) → (S ∧ L) S → T ~T ∴ R ~T ∴→ ~S by Modus Tollens ~S → ~(S ∧ L) by definition of the conjunction ~(S ∧ L) → ~(~R ∨ ~F) by Modus Tollens ~(~R ∨ ~F) ≡ (R ∧ F) by DeMorgan’s Laws (R ∧ F) → R by Specialization Therefore, the argument is valid. 5. a. ~s → ~r b. s → r c. ~r → ~s 6. b and c are true. 7. a. 1589 b. 14eb c. 111010101101001111 8. 01110001...
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 Spring '08
 Foster
 Addition, Modus tollens, rain foggy Sailing, Modus Tollens ~S, Lifesaving Demo Trophy

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