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# Math 121 Unit 3: Logic Review MATH 121 001

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This 13 page Study Guide was uploaded by marleeelyse on Monday October 17, 2016. The Study Guide belongs to MATH 121 001 at West Virginia University taught by Seth Cole in Fall 2016. Since its upload, it has received 4 views. For similar materials see Introduction to Mathematics in Mathematics at West Virginia University.

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Date Created: 10/17/16

1. State the Formal Name for each connective: Fill out the following table Formal Name Symbol Read Symbolic Form ~ “Not” ~P Λ “And” P ΛQ V “Or” P VQ → “If … P → Q then …” ↔ “If and only if” P ↔ Q The following table represents the Dominance of Connectives (order of operations). You do not need to fill out this table. Least Dominant 1. Negation Evaluate ~ First 2. Conjunction Disjunction 3. Conditional → Most Dominant 4. Biconditional Evaluate ↔ Last 2. Let p: I watch soap operas and q: I remember to record the soap operas everyday • Write the compound statement in words: ~p ↔~q • Write the compound statement using letters P, Q, and R and logical connectors: “If I go to the pool and it is not sunny, then I will not get a suntan.” 3. What is the order you would complete this symbolic statement: ~R→P Λ Q. Put parentheses in to show the order. Is this compound statement a negation, conjunction, disjunction, conditional or biconditional? 4. Complete the truth table below P Q P ΛQ Case 1 T T Case 2 T F Case 3 F T Case 4 F F 5. Give a summary of when a conjunction is true and when it is false. 6. Complete the truth table below P Q P VQ T T T F F T F F 7. Give a summary of when a disjunction is true and when it is false. 8. Complete the truth table below P Q P→Q T T T F F T F F 9. Give a summary of when a conditional is true and when it is false. 10. Complete the truth table below P Q P↔Q T T T F F T F F 11.Give a summary of when a biconditional is true and when it is false. PQ ~ P 12. Complete a truth table for the following: ~ PQ R 13.Complete a truth table for the following: (Q R) (~ PR) 14. What is the truth value of the statement when P is true, Q is false, and R is true. R ~ P ~ Q 15. Evaluate If P is True, Q is True and R is False 16.Circle which of the following make the statement (~PVQ) à Q False: 1. P true, Q true 2. P true, Q false 3. P false, Q true 4. P false, Q false 17.A _________________________ is a compound statement that is always false. 18.A ________________________ is a compound statement that is always true. 19.An _______________________ is a conditional statement that is a tautology. (PQ)(PQ) 20. Is the following a tautology, contradiction, implication, or none of the above? , 21. Two statements are __________________________, symbolized by if both statements have exactly the same truth values in the answer column of the truth tables. a. Thus to determine if two statements are equivalent, construct truth tables for both and compare the answer columns. (P Q) (Q P). 22. Determine if P↔Q is equivalent to Show your work. 23.Use the fact that P Q is equivalent to P V Q to write an equivalent form of the given statement a. “If Erin selects a new textbook, then she will have to write a new syllabus” 2. ~ (PQ)~ P ~ Q1. ~ (PQ) ~ P ~ Q DeMorgan’s Laws for Logic provide two useful equivalences of statements. 24.Fill in the following table Name Symbolic Form Conditional P→Q Converse of conditional Inverse of conditional Contrapositive of conditional 25.Write the converse, inverse and contrapositive of the following statement in English and using mathematical statements and connectives: i. If I do not answer my emails, then students are upset. 26.A _________________________________ consists of a set of premises and a conclusion. i. The following is an example of a symbolic argument: Premise 1: If Jason is a singer, then he is famous. Premise 2: Jason is a singer. Conclusion: Therefore, Jason is famous. 27.An argument is ________________________ when the conclusion necessarily follows from a given set of premises. 28.An argument is ______________________________ or a ________________________ when the conclusion does not necessarily follow from the given set of premises. 29.Fill in the following table with the symbolic representation of each argument Law of Law of Law of Syllogism Disjunctive Detachment Contraposition Syllogism Fallacy of the Converse Fallacy of the Inverse 30.Determine whether the argument is valid or invalid. Show your work or explain your answer. If it is not cold, then graduation will be held outside. It is cold Therefore, graduation will not be held outside 31.Determine whether the argument is valid or invalid. Show your work or explain your answer. If you pass general chemistry, then you can take organic chemistry You pass general chemistry Therefore, you can take organic chemistry 32.Determine whether the argument is valid or invalid. Show your work or explain your answer. If Erica Kane teaches this course, then I will get a passing grade. I did not get a passing grade. Therefore, Erica Kane did not teach the course. Relating circuits to logic::T (true) represents a closed switch (or current flow), F (false) represents an open switch (or no current flow). 33.Two types of circuits that are connected to symbolic statements and logic: a. In a ______________________________ the current can take only one path. b. In a ______________________________ there are two or more paths the current can take. 34.Fill in the following blanks relating a series circuit to logic a. Case 1: Both switches are closed; that is, p is T and q is T. The light is __________. b. Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is ____. c. Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is ____. d. Case 4: Both switches are open; that is, p is F and q is F. The light is ___________. 35.A series circuit is similar to a _________________statement in logic 36.Fill in the following blanks relating a parallel circuit to logic a. Case 1: Both switches are closed; that is, p is T and q is T. The light is ____________. b. Case 2: Switch p is closed and switch q is open; that is, p is T and q is F. The light is ____. c. Case 3: Switch p is open and switch q is closed; that is, p is F and q is T. The light is ____. d. Case 4: Both switches are open; that is, p is F and q is F. The light is ____________. 37.A parallel circuit is similar to a _________________statement in logic. 38.Write a symbolic statement that represents the circuit and construct a truth table to determine when the light will be on. 39.Draw a switching circuit that represents ~PΛ (QVR) 40.____________________________________________ are two circuits that have equivalent corresponding symbolic statements. a. Sometimes two circuits that look very different will actually have the exact same conditions under which the light will be on. b. The truth tables will have identical answer columns. c. Hence, we can determine two circuits are equivalent if their corresponding truth tables have identical answer columns. 41.Determine whether the two circuits are equivalent.

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