MTH 330 Success Begins / snaptutorial.com

1. MTH 330 Week 1 Individual Assignment For more classes visit www.snaptutorial.com Ch. 1: Section 1.1, Exercise 5 Ch. 1: Section 1.2, Exercise 7 Ch. 2: Section 2.1, Exercises 3, 6, & 8 Ch. 2, Section 2.2, Preview Activity 3 Ch. 2; Section 2.2, Activity 2.10 (Item 1) ========================= MTH 330 Week 1 Quiz For more classes visit www.snaptutorial.com 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.

2. (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. right can be replaced by the word or words In a logical implication, the double-shafted arrow pointing to the (a) “and.” (b) “if.” (c) “if and only if.” (d) “implies.”

3. 1. of three sentences, each of which can attain either the value T or the value F? How many possible combinations of truth values are there for a set (a) 2 (b) 4 (c) 8 (d) 16 1. 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 Suppose you observe, “It is not sunny today, and it’s not warm.” (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. You demonstrate that my supposed rule has at least one exception. This shows that Imagine that I claim a certain general statement is a rule of logic. (a) it is not a law of logic.

4. (b) it violates the commutative law. (c) it violates the law of implication reversal. (d) it demonstrates that a disjunction implies logical falsity. 1. table? Look at Table 1-16. What, if anything, is wrong with this truth (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. derivation? What, if anything, can be done to make Table 1-16 show a valid

5. (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. 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 Imagine that someone says to you, “If I am a human and I am not a

6. (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. part of this sentence after the quantifier Suppose we are given a sentence in symbolic form: (∃x) Px. The (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.

7. 1. wffs. Which of the following is not a wff? Suppose F, G, and H are complicated sentences, but all three are (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.

8. (c) We are prisoners. (d) Jane drives a truck. 1. 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: Let the predicate symbol W stand for “is a widget,” and let the (∀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. in Fig. 2-9 can apply to this situation? Consider the scenario of Question 6. Which of the Venn diagrams (a) A (b) B (c) C (d) None of the diagrams (A), (B), or (C) can apply.

9. 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. this sentence can best be described as Consider the statement “I created a TIFF image.” The structure of (a) SVO. (b) SV. (c) an existential quantifier. (d) a universal quantifier. ======================== MTH 330 Week 2 Individual Assignment

10. For more classes visit www.snaptutorial.com Preview Activity 3 (Item 1) Section 3.1 Exercise 15 Section 3.3 Exercise 5 Section 3.3 Exercise 17 Section 5.1 Exercise 3 Section 5.2 Exercise 12 ========================= MTH 330 Week 2 Quiz For more classes visit www.snaptutorial.com MTH 330 Week 2 Quiz ====================== MTH 330 Week 3 Individual Assignment Mathematical Terms Worksheet For more classes visit

11. www.snaptutorial.com MTH 330 Week 3 Individual Assignment Mathematical Terms Worksheet ===================== MTH 330 Week 3 Individual Assignment For more classes visit www.snaptutorial.com Ch. 6. Section 6.1-Preview Activity 3 Ch. 6. Section 6.1 Activity 6.6 #1-#4 Ch 6. Section 6.3 Exercise #1 & #4 ========================== MTH 330 Week 3 Quiz For more classes visit www.snaptutorial.com Chapter 6 Quiz 1. What is the cardinality of the empty set?

12. (a) 0 (b) 1 (c) Infinity (d) It is not defined. 1. An equivalence relation is (a) symmetric. (b) distributive. (c) denumerable. (d) All of the above 1. of propositional logic can be applied directly to Solution 6-1 (treating Solution 6-1 as a theorem), in order to solve Problem 6-2 by the second method mentioned? Look back at Chapter 1 if you must. Look back at Problems 6-1 and 6-2, and their solutions. Which rule (a) DeMorgan’s law for implication. (b) The law of implication reversal. (c) The commutative law for disjunction. (d) The commutative law for conjunction.

13. 1. you are told that you’ll get a chance to provide the reason for the statement. Now is the time! What is the reason? At the end of Solution 6-3 and in the next-to-last line of Table 6-3, (a) The element u has not been specified, so we cannot say it is in the intersection of two specific sets. (b) We are making a generalization about the element u, so we cannot say anything specific about it. (c) No matter what u happens to be, it can’t be in a set that has no elements. (d) Sets S and T are not the same, so obviously element u cannot be in both of them. 1. the proof and in Table 6-5A, one of the steps makes the claim that r ∈ Q ∪ X. In the second part of the proof and in Table 6-5B, one of the steps says that s ∈ S ∪ Y. The reason in both cases is the same, but it’s left out, and you’re told you’ll get a chance to identify it. Your chance has come! What is the reason for this statement in both parts of the proof? Refer to Solution 6-5 and Tables 6-5A and 6-5B. In the first part of (a) It follows from the definition of logical disjunction. (b) It follows from the definition of logical implication. (c) It follows from the definition of set intersection. (d) It follows from the definition of set union.

14. 1. statements says that h is an integer (that is, h ∈ Z). What allows us to make this claim? Refer to Solution 6-6 and Table 6-6. In this proof, one of the (a) The product-of-integers axiom. (b) The product-of-fractions axiom. (c) The sum-of-integers axiom. (d) The sum-of-fractions axiom. 1. that −c = −1 × c. What allows us to make this claim? Refer to Solution 6-7 and Table 6-7. One of the statements says (a) The additive-inverse axiom. (b) The sum-of-integers axiom. (c) The product-of-integers axiom. (d) The definition of a rational number. 1. that (ac)/(bd) ∈ Q. A similar situation occurs in Solution 6-9 and Table 6-9, where one of the statements says that (ad)/(bc) ∈ Q. What allows us to make these claims? Refer to Solution 6-8 and Table 6-8. One of the statements says

15. (a) The additive-inverse axiom. (b) The sum-of-integers axiom. (c) The product-of-integers axiom. (d) The definition of a rational number. 1. the following: Refer to Solution 6-10 and Table 6-10. One of the statements says (r + s)t + (r + s)u = t(r + s) + u(r + s) After this statement, you’re told you’ll get a chance to provide the reason. Your chance has come! What allows us to make this claim? (a) The commutative axiom for addition, applied twice. (b) The commutative axiom for multiplication, applied twice. (c) The equality axiom. (d) The distributive axiom. 1. says that a certain component of the equality axiom is used repeatedly to come to the conclusion shown. You’re told you’ll get a chance to identify that component. Your chance has come! Which component is it? Refer again to Solution 6-10 and Table 6-10. In the last step, it (a) The reflexive property. (b) The symmetric property.

16. (c) The transitive property. (d) The equivalence property. ================== MTH 330 Week 4 Individual Assignment For more classes visit www.snaptutorial.com MTH 330 Week 4 Individual Assignment ======================== MTH 330 Week 4 Quiz For more classes visit www.snaptutorial.com MTH 330 Week 4 Quiz ======================= MTH 330 Week 5 Individual Assignment For more classes visit www.snaptutorial.com

17. MTH 330 Week 5 Individual Assignment ======================== MTH 330 Week 5 Quiz For more classes visit www.snaptutorial.com MTH 330 Week 5 Quiz ================================