Chapter 1 1. � The conjunction of three sentences is false (a) if and only if all three sentences are false. (b) if and only if at least one of the sentences is false. (c) if and only if at least two of the sentences are false. (d) under no circumstances, because a conjunction can’t be defined for more than two sentences. 1. � The disjunction of three sentences is false (a) if and only if all three sentences are false. (b) if and only if at least one of the sentences is false. (c) if and only if at least two of the sentences are false. (d) under no circumstances, because a disjunction can’t be defined for more than two sentences. 1. � In a logical implication, the double-shafted arrow pointing to the right can be replaced by the word or words (a) “and.”� (b) “if.”� (c) “if and only if.”� (d) “implies.”� 1. � How many possible combinations of truth values are there for a set of three sentences, each of which can attain either the value T or the value F? (a) 2 (b) 4 (c) 8 (d) 16 1. � Suppose you observe, “It is not sunny today, and it’s not warm.”� Your friend says, “The statement that it’s sunny or warm today is false.”� These two sentences are logically equivalent, and this constitutes a verbal example of (a) one of DeMorgan’s laws. (b) the law of double negation. (c) the commutative law for conjunction. (d) the law of implication reversal. 1. � Imagine that I claim a certain general statement is a rule of logic. You demonstrate that my supposed rule has at least one exception. This shows that (a) it is not a law of logic. (b) it violates the commutative law. (c) it violates the law of implication reversal. (d) it demonstrates that a disjunction implies logical falsity. 1. � Look at Table 1-16. What, if anything, is wrong with this truth table? (a) Not all possible combinations of truth values are shown for X, Y, and Z. (b) The entries in the far right-hand column are incorrect. (c) It is impossible to have a logical operation such as (X ∨ Y) & Z. (d) Nothing is wrong with Table 1-16. 1. � What, if anything, can be done to make Table 1-16 show a valid derivation? (a) Nothing needs to be done. It is correct as it is. (b) In the top row, far-right column header, change the ampersand (&) to a double-shafted arrow pointing to the right (⇒). (c) In the far-left column, change every T to an F, and change every F to a T. (d) In the first three columns, change every T to an F, and change every F to a T. 1. � A rule or law that has been proven (a) can’t be used to prove future theorems, because all theorems must be proven directly from an original set of rules. (b) can be used to prove future theorems, as long as truth tables are avoided. (c) can be used to prove future theorems, but only by means of truth tables. (d) can be used to prove future theorems. 1. � Imagine that someone says to you, “If I am a human and I am not a human, then the moon is made of Swiss cheese.”� (Forget for a moment that this person has obviously lost contact with the real world.) This is a verbal illustration of the fact that (a) implication can’t be reversed. (b) DeMorgan’s laws don’t always hold true. (c) conjunction is not commutative. (d) a contradiction implies logical falsity. Chapter 2 1. � Suppose we are given a sentence in symbolic form: (∃x) Px. The part of this sentence after the quantifier (a) is an SV sentence. (b) is an SVO sentence. (c) is an SLVC sentence. (d) might be an SV, SVO, or SLVC sentence; we don’t know unless we are told what P stands for. 1. � If Q is a sentence in propositional logic, then (a) Q is a wff. (b) Q is not a wff. (c) Q contains an existential quantifier. (d) Q contains a universal quantifier. 1. � Suppose F, G, and H are complicated sentences, but all three are wffs. Which of the following is not a wff? (a) ¬(F & G) ⇒ H (b) ¬F & ¬G & ¬H (c) ¬F ¬&G ¬&H (d) F ∨ G ∨ ¬H 1. � Which of the following is an example of an SLVC sentence? (a) I know. (b) Jim runs to the Post Office. (c) We are prisoners. (d) Jane drives a truck. 1. � Which of the following is an example of an SV sentence? (a) I know. (b) Jim runs to the Post Office. (c) We are prisoners. (d) Jane drives a truck. 1. � Let the predicate symbol W stand for “is a widget,”� and let the predicate symbol D stand for “is a doodad.”� Imagine that there are lots of widgets and lots of doodads lying around. Let z be a variable. Suppose we know the following statement is true: (∀z) (Wz ⇒ Dz) Based on this fact, of which of the following statements can we be certain? (a) (∀z) (Dz ⇒ Wz) (b) ¬(∀z) (Dz ⇒ Wz) (c) (∃z) (Wz & Dz) (d) All of the above 1. � Consider the scenario of Question 6. Which of the Venn diagrams in Fig. 2-9 can apply to this situation? (a) A (b) B (c) C (d) None of the diagrams (A), (B), or (C) can apply. 1. � In an SVO sentence, the subject is always (a) a noun. (b) a verb. (c) an adjective. (d) a wff. 1. � A wff cannot contain (a) both negation and disjunction. (b) both negation and conjunction. (c) both constants and variables. (d) a variable all by itself, and nothing else. 1. � Consider the statement “I created a TIFF image.”� The structure of this sentence can best be described as (a) SVO. (b) SV. (c) an existential quantifier. (d) a universal quantifier.
Previous answers to this question
This is a preview of an assignment submitted on our website by a student. If you need help with this question or any assignment help, click on the order button below and get started. We guarantee authentic, quality, 100% plagiarism free work or your money back.
Get The Answer