NB: The alphabets in bold face (A - J) group the questions under the same kind;

Question

NB: The alphabets in bold face (A - J) group the questions under the same kind; The bracket { } indicates the score (3 - 10) assigned to the question; & The bracket [ ] shows the question number (01 - 21). A. (a) (b) {3} [01] Determine whether the argument is sound or unsound; and Explain your answers by referring to the two constituent properties assigned to their components. {3} [02] 1. 2. 3. George Washington is one of the Founding Fathers. George Washington crossed the Delaware. Therefore, George Washington is the first President. 1. 2. 3. A rectangle has five sides. This letter-sized paper is a rectangle. Therefore, the paper has five sides. B. (a) Determine whether the argument is deductive or inductive, and (b) Explain your answer by referring to all of the three criteria on inference. {3} [03] Rutgers, Princeton, and NYU are all located on the East Coast. All major universities must be located on the East Coast. {3} [04] Anyone who is good at logic is a critical thinker. I am good at logic. So I am a critical thinker. C. (a) Identify atomic sentences employed in the compound sentence, and assign sentence constants (i.e., sentence abbreviations); and (b) Symbolize the compound sentence using the sentence constants and the appropriate connectives. {3} [05] For the first opening piece in tonight’s concert, the New York Philharmonic will perform an Overture by Beethoven or a Divertissement by Mozart. {3} [06] Only if you do exercises carefully and study hard can you earn a good grade. D. Fill the blanks in the following sentences with P, Q, X, or Y as defined below. {3} [07] ___________ is sufficient for _____________. P: 'Henry' is an animal. Q: 'Henry' is a man. {3} [08] __________ is necessary for ______________. X: Rutgers is in New Jersey. Y: Rutgers is in US. E. Show how truth tables are used to answer the questions on the following two sentences. {3} [09] Determine the modal nature of the sentence: (A•B) ? (~A?~B) {3} [10] Determine whether the two sentences are equivalent or not: P?Q / ~Q?~P F. Show that the following (formalized) arguments are valid by deriving conclusions from the given premises by utilizing inference rules. {5} [11] C: S ------------------------------------------------------ 1: P?Q 2: R?P 3: (Q•~R) ? (S•~R) 4: ~P ------------------------------------------------------ {5} [12] C: ~Y ? ~X ------------------------------------------ 1. (Q ? U) ? Y 2. X ? (Q•T) ------------------------------------------ {5} [13] C: ~A ------------------------------------------- 1. ~C ? ~M 2. A ? (M•N) 3. C?M ------------------------------------------- {5} [14] C: P ? Q -------------------------------------------- 1: P?~R 2: ~Q ? R 3: P?~Q -------------------------------------------- G. Do the following 3 things respectively with each of the two sentences given below: 1. Translate it by using the defined predicate symbols and a quantifier; 2. Transform it into an equivalent statement with a quantifier different from the one used in the 1st translation (by applying QN); and 3. Articulate the corresponding sentence of the 2nd translation in ordinary English. {5} [15] Not all dogs bark. D: being a dog B: barking {5} [16] All philosophers are neither impractical nor unrealistic. P: being a philosopher I : being impractical U: being unrealistic H. Do the 2 things respectively with the three syllogistic arguments given below: 1. Translate the following arguments by using predicate letters (as defined below), constant variables, and quantifiers; and 2. Show that they are logically valid by deriving the conclusion from the premises. {6} [17] P1: All humans have inviolable rights. P2: Not all creatures have inviolable rights. C: Therefore, there are many creatures that cannot be humans. H: being a human I : having inviolable rights C: being a creature {7} [18] P1: There is no human being who is not mortal. P2: No angels are mortal. C: Therefore, no human beings are angels. H: being a human M: being mortal A: being an angel I. Choose one of the two conceptual questions, and answer it as elaborately as you can: {10} [19] What are the instances of non-truth-functional compound sentences, and why do they become non-truth-functional (as opposed to truth-functional)? {10} [20] What does it mean to say that an argumentation in a civilized (rational) society takes place in an interactive environment? And when does an argument become fallacious in a way that it is question-begging?

Explanation / Answer

In order for an argument to be sound the argument (a). must be valid and (b). have all premises be true. If either of these conditions is false then the argument is unsound. In the first argument, the premise 1). George Washington is one of the Founding Fathers and 2). George Washington crosses the Delaware are true; however, the conclusion “George Washington is the first President” does not reflect these premises. Inference is derived from the truth and validity of the argument within the conclusion. That being said, this argument is unsound as even though it has all true premises, it is still an invalid argument. In the second argument, the inference is correctly derived from the premises, causing the argument to be valid; however, the premise in the argument that “A rectangle has five sides” is false, because A five-sided shape is called a pentagon and the six-sided shape is a hexagon. That being said, even though the argument is valid, it is still unsound as not all the premises are true.

Please remind this note: Answering to many questions is against to CHEGG RULE

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