Chapter 1\t1. \ufffd The conjunction of three sentences is false\t(a) if and only if all three sentences are false.\t(b) if and only if at least one of the sentences is false.\t(c) if and only if at least two of the sentences are false.\t(d) under no circumstances, because a conjunction can’t be defined for more than two sentences.\t\u00a0\t1. \ufffd The disjunction of three sentences is false\t(a) if and only if all three sentences are false.\t(b) if and only if at least one of the sentences is false.\t(c) if and only if at least two of the sentences are false.\t(d) under no circumstances, because a disjunction can’t be defined for more than two sentences.\t\u00a0\t1. \ufffd In a logical implication, the double-shafted arrow pointing to the right can be replaced by the word or words\t(a) “and.”\ufffd\t(b) “if.”\ufffd\t(c) “if and only if.”\ufffd\t(d) “implies.”\ufffd\t\u00a0\t1. \ufffd 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?\t(a) 2\t(b) 4\t(c) 8\t(d) 16\t\u00a0\t1. \ufffd Suppose you observe, “It is not sunny today, and it’s not warm.”\ufffd Your friend says, “The statement that it’s sunny or warm today is false.”\ufffd These two sentences are logically equivalent, and this constitutes a verbal example of\t(a) one of DeMorgan’s laws.\t(b) the law of double negation.\t(c) the commutative law for conjunction.\t(d) the law of implication reversal.\t\u00a0\t1. \ufffd 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\t(a) it is not a law of logic.\t(b) it violates the commutative law.\t(c) it violates the law of implication reversal.\t(d) it demonstrates that a disjunction implies logical falsity.\t\u00a0\t\u00a0\t1. \ufffd Look at Table 1-16. What, if anything, is wrong with this truth table?\t(a) Not all possible combinations of truth values are shown for X, Y, and Z.\t(b) The entries in the far right-hand column are incorrect.\t(c) It is impossible to have a logical operation such as (X \u2228 Y) & Z.\t(d) Nothing is wrong with Table 1-16.\t\u00a0\t\u00a0\t\u00a0\t\u00a0\t\u00a0\t1. \ufffd What, if anything, can be done to make Table 1-16 show a valid derivation?\t(a) Nothing needs to be done. It is correct as it is.\t(b) In the top row, far-right column header, change the ampersand (&) to a double-shafted arrow pointing to the right (\u21d2).\t(c) In the far-left column, change every T to an F, and change every F to a T.\t(d) In the first three columns, change every T to an F, and change every F to a T.\t\u00a0\t\u00a0\t1. \ufffd A rule or law that has been proven\t(a) can’t be used to prove future theorems, because all theorems must be proven directly from an original set of rules.\t(b) can be used to prove future theorems, as long as truth tables are avoided.\t(c) can be used to prove future theorems, but only by means of truth tables.\t(d) can be used to prove future theorems.\t\u00a0\t1. \ufffd 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.”\ufffd (Forget for a moment that this person has obviously lost contact with the real world.) This is a verbal illustration of the fact that\t(a) implication can’t be reversed.\t(b) DeMorgan’s laws don’t always hold true.\t(c) conjunction is not commutative.\t(d) a contradiction implies logical falsity.\t\u00a0\tChapter 2\t1. \ufffd Suppose we are given a sentence in symbolic form: (\u2203x) Px. The part of this sentence after the quantifier\t(a) is an SV sentence.\t(b) is an SVO sentence.\t(c) is an SLVC sentence.\t(d) might be an SV, SVO, or SLVC sentence; we don’t know unless we are told what P stands for.\t\u00a0\t1. \ufffd If Q is a sentence in propositional logic, then\t(a) Q is a wff.\t(b) Q is not a wff.\t(c) Q contains an existential quantifier.\t(d) Q contains a universal quantifier.\t\u00a0\t1. \ufffd Suppose F, G, and H are complicated sentences, but all three are wffs. Which of the following is not a wff?\t(a) \u00ac(F & G) \u21d2 H\t(b) \u00acF & \u00acG & \u00acH\t(c) \u00acF \u00ac&G \u00ac&H\t(d) F \u2228 G \u2228 \u00acH\t\u00a0\t1. \ufffd Which of the following is an example of an SLVC sentence?\t(a) I know.\t(b) Jim runs to the Post Office.\t(c) We are prisoners.\t(d) Jane drives a truck.\t\u00a0\t1. \ufffd Which of the following is an example of an SV sentence?\t(a) I know.\t(b) Jim runs to the Post Office.\t(c) We are prisoners.\t(d) Jane drives a truck.\t\u00a0\t1. \ufffd Let the predicate symbol W stand for “is a widget,”\ufffd and let the predicate symbol D stand for “is a doodad.”\ufffd 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:\t(\u2200z) (Wz\u00a0\u21d2 Dz)\tBased on this fact, of which of the following statements can we be certain?\t(a) (\u2200z) (Dz \u21d2 Wz)\t(b) \u00ac(\u2200z) (Dz \u21d2 Wz)\t(c) (\u2203z) (Wz & Dz)\t(d) All of the above\u00a0\t1. \ufffd Consider the scenario of Question 6. Which of the Venn diagrams in Fig. 2-9 can apply to this situation?\t(a) A\t(b) B\t(c) C\t(d) None of the diagrams (A), (B), or (C) can apply.\u00a0\t1. \ufffd In an SVO sentence, the subject is always\t(a) a noun.\t(b) a verb.\t(c) an adjective.\t(d) a wff.\u00a0\t1. \ufffd A wff cannot contain\t(a) both negation and disjunction.\t(b) both negation and conjunction.\t(c) both constants and variables.\t(d) a variable all by itself, and nothing else.\u00a0\t1. \ufffd Consider the statement “I created a TIFF image.”\ufffd The structure of this sentence can best be described as\t(a) SVO.\t(b) SV.\t(c) an existential quantifier.\t(d) a universal quantifier.<\/p>\n","protected":false},"excerpt":{"rendered":"
Chapter 1 1. \ufffd 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 Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-229639","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/229639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=229639"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/229639\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=229639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=229639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=229639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}