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A series of questions and answers related to propositional logic, focusing on the construction and interpretation of truth tables. It covers concepts such as tautologies, self-contradictions, logical equivalence, and consistency. The exercises require the application of truth tables to determine the validity and relationships between different logical statements. The document also includes real-world examples and scenarios to illustrate the application of propositional logic in various contexts, such as political statements and scientific research. It is designed to test and reinforce understanding of fundamental principles in logic and critical thinking, providing a comprehensive review of key concepts and techniques.
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(~K ⊃ H) ≣ ~(H v K) - ANSF T F F T F T F F T T T F F T T F F T F self-contradictory (E⊃C) ⊃ L - ANSdoes not apply consistent (G⊃G) ⊃ G - ANST T T F contingent (M⊃P) v (P⊃M) - ANST T T F T T T T F T T T tautologous (S⊃R) • (S • ~R) - ANST F F F F F T T
self-contradictory [(C⊃D) • ~C] ⊃ ~D - ANST F F T F F F F T T T T T F F T T T T T contingent [(E⊃F) ⊃ F] ⊃ E - ANST T T F T T T T F T F T contingent [(F v E) • (G v H)] ≣ [(G • E) v (F • H)] - ANST T T T T T T T T T T T T F T T T T F T T T F F T F F F T T T T F T T T T T F F F F T T T T F T T T F F T F F F T T T T T T F
self-contradictory [(U • (T v S)] ≣ [(~T v ~U) • (~S v ~U)] - ANST T F F F F F F F F T T F F F F F T T F T T F T T F F F F F F F F T T F T T T F F T F F T T T F T T F T F F T T T T T T F T F T T T T F T T F F F T T T T T T T self-contradictory [(Z⊃X) • (X v Z)] ⊃ X - ANST T T T F F T T T T T T T F F T tautologous [G ⊃ (N ⊃ ~G)] • [(N ≣ G) • (N v G)] - ANSF F F F T T T T T F F F F T T T T F F F T T T T F T F F self-contradictory
contingent {[(G • N) ⊃ H] • [(G ⊃ H) ⊃ P]} ⊃ (N⊃P) - ANST T T T T T T T T F T F T F T F F F T T T T F F F T T F F T T T T T T F T F T F T T F T T F T T T F T T F T T T F T T T T T T F T F T F T F F T T T T T T F T F T F T F F T T T T T T F T F T F T T
Automotive expert Frank Goodbody has this to say about Japanese imports: "If Mitsubishi is the sportiest, then both Toyota is the most trouble- free and Isuzu is not the lowest priced. If Isuzu is the lowest priced, then both Toyota is not the most trouble-free and Mitsubishi is the sportiest." - ANSYes Isuzu is not the lowest priced. Christina and Thomas are having a discussion about their plans for the evening. Christina: "If you don't love me, then I'm certainly not going to have sex with you." Thomas: "Well, that means that if I do love you, then you will have sex with me, right?" - ANSThomas is not correct; the two statements are not logically equivalent. Cindy, Jane, and Amanda witnessed a bank robbery. At trial, Cindy testified that Lefty did not enter the bank, and if Howard pulled a gun, then Conrad collected the money. Jane testified that if Howard did not pull a gun, then Lefty entered the bank. Amanda testified that if Conrad collected the money, then Howard pulled a gun. - ANSYes Lefty did not enter the bank, Howard pulled a gun, and Conrad collected the money. Eric Carson sums up his beliefs about God as follows: "God exists if and only if either life is meaningful or the soul is not immortal. God exists and the soul is immortal. If God exists, then life is not meaningful." - ANSEric's beliefs are inconsistent; therefore, they do not make sense.
F • M - ANSdoes not apply inconsistent G • (E v P) - ANScontradictory H • (K v J) - ANSlogically equivalent H ≣ ~G - ANScontradictory M ⊃ (K⊃P) - ANSlogically equivalent N • (A v ~E) - ANSdoes not apply inconsistent N ⊃ (N⊃N) - ANST T T T tautologous Nicole Evans expresses her philosophy as follows: "If the mind is identical to the brain, then personal freedom does not exist and humans are not responsible for their actions. If personal freedom does not exist, then the mind is identical to the brain. Either humans are responsible for their actions or the mind is not identical to the brain. If personal freedom exists, then humans are responsible for their actions." - ANSYes
Compucel expands production. The other claims that Datapro will cut its workforce, and Compucel will expand production if and only if Netmark introduces a new product. - ANSYes Datapro will cut back its work force. W ≣ (B • T) - ANSdoes not apply inconsistent Z • (C≣P) - ANSdoes not apply inconsistent
