Determining Truth Value of Complex Statements , Determining Validity of Propositional Arguments
Determining Truth Value of Complex Statements , Determining Validity of Propositional Arguments
Section 1 – Determining Truth Value of Complex Statements For the following arguments, determine the truth value of the complex statement. Assume A, B, C are true and X, Y, Z are false. 1. B •Z 2. X v ~Y 3. ~C v Z 4. B ~Z 5. (A v B) Z 6. ~(A •Z) 7. ~B v (Y A) 8. A ~(Z v ~Y) 9. (A •Y) v (~Z •C) 10. ~(X v ~B) •(~Y vA) Section 2 – Determining Validity of Propositional Arguments For the following arguments, (a) provide the argument in propositional form. Be sure to indicate which letters represent which propositions. (b) Provide a truth table for the argument; (c) State whether the argument is valid or invalid. 1. If X is an even number, then X is divisible by 2. But X is not divisible by 2. Thus, X is not an even number. 2. Eddie can vote if and only if he is registered. But Eddie is not registered. Therefore, Eddie cannot vote. 3. If animals feel pain or learn from experience, then animals are conscious. Animals do not feel pain. Animals do not learn from experience. Therefore, animals are conscious. 4. Either the USS Arizona or the USS Missouri was not sunk in the attack on Pearl Harbor. Therefore, it is not the case that either the USS Arizona or the USS Missouri was sunk in the attack on Pearl Harbor. 5. I am hungry and I am not hungry. Therefore, I will eat my shoe. Section 3 – 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. (a) Show whether it possible that all three witnesses told the truth. (b) Assuming that all witnesses told the truth, what can we conclude about Lefty, Howard, and Conrad?
