Question 1 A biconditional statement whose main components are consistent statem

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Question 1 A biconditional statement whose main components are consistent statements is itself a: coherency contingency self-contradiction unable to determine from the information given tautology 3 points Question 2 A biconditional statement whose main components are equivalent statements is itself a: self-contradiction coherency unable to determine from the information given contingency tautology 3 points Question 3 Choose which symbol to use for “it is not the case that,” “it is false that,” and “n’t.” ~ • 3 points Question 4 A conditional statement where both the antecedent and consequent are equivalent statements is itself a: unable to determine from the information given tautology coherency contingency self-contradiction 3 points Question 5 Identify which of the following is a correct symbolization of the following statement. If the shoe fits, then one has to wear it. F • W F W F F W F W 3 points Question 6 Identify which of the following is a correct symbolization of the following statement. If you say it cannot be done, you should not interrupt the one doing it. ~S ~I ~S • ~I S ~I ~S ~I ~S ~I 3 points Question 7 Identify the main connective in the following statement. L [(W L) ~(Y T)] ~ • 3 points Question 8 In the truth table for the statement form ~(p p), the column of truth values underneath the main connective should be FF. Therefore, this statement form is a: contingency contradiction tautology equivalency self-contradiction 3 points Question 9 In the truth table for the statement form p q, the column of truth values underneath the main connective should be: TFFF TFFT TTTF TTFF TFTT 3 points Question 10 In the truth table for the statement form p • q, the column of truth values underneath the main connective should be TFFF. Therefore, this statement form is a: tautology contingency contradiction equivalency self-contradiction 3 points Question 11 Symbolize “both not p and not q.” ~( p • q) ~p • q ( p q) • (~p q) ( p q) • ~( p • q) ~p • ~q 3 points Question 12 The connective used for biconditionals is: ~ • 3 points Question 13 The statement form p q is: not actually a statement form a conjunction a conditional a disjunction a biconditional 3 points Question 14 The following argument is an instance of one of the five equivalence rules DM, Contra, Imp, Bicon, Exp. Identify the rule. ~(R U) ~(T O) ~[(R U) • (T O)] Bicon DM Exp Contra Imp 3 points Question 15 The following argument is an instance of one of the five equivalence rules DM, Contra, Imp, Bicon, Exp. Identify the rule. ~S ~(~G U) (~G U) S Bicon Exp DM Imp Contra 3 points Question 16 The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule. (G R) • (E S) [(G R) • E] [(G R) • S] Com Assoc DN Dist Taut 3 points Question 17 The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule. (~N D) (T • K) [(~N D) T] • [(~N D) K) Assoc Dist Taut Com DN 3 points Question 18 The following argument is an instance of one of the five equivalence rules Taut, DN, Com, Assoc, Dist. Identify the rule. ~W • O ~~~W • O DN Com Assoc Taut Dist 3 points Question 19 The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. [(G • R) (S P)] (N • G) ~(N • G) ~[(G • R) (S P)] HS MT Conj DS MP 3 points Question 20 The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. M O (M O) (F • R) F • R MT DS MP HS Conj 3 points Question 21 The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. [(P T) • (H • N)] (T ~S) (T ~S) [(H E) R] [(P T) • (H • N)] [(H E) R] MP DS Conj MT HS 3 points Question 22 The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. T H ~H T MT DS HS Conj MP 3 points Question 23 The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form. (K N) (O • W) ~(O • W) (K N) HS Conj DS MT MP 3 points Question 24 The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form. M • S M M • (M • S) Add Simp Conj DD CD 3 points Question 25 The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form. (X M) • (R A) X R M A DD Conj Add CD Simp 3 points Question 26 The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form. (P R) • (V V) ~R ~V ~P ~V CD DD Simp Add Conj 3 points Question 27 The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form. [(~S U) (T E)] • [(D E) ~N] (~S U) (D E) (T E) ~N DD Simp Add Conj CD 3 points Question 28 The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD. Identify the form. [(S P) (C I)] • [(F ~C) M] (S P) (F ~C) (C I) M Simp CD DD Add Conj 3 points Question 29 Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? A (J S) ~J S A None—the argument is valid. A: F J: F S: T A: T J: F S: T A: T J: T S: F A: T J: T S: T 3 points Question 30 Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? (E • ~H) G ~(H G) ~E None—the argument is valid. E: T H: F G: T E: T H: T G: F E: F H: F G: F E: T H: T G: T 3 points Question 31 Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? (Z Y) X Z W ~Y ~W V W Z: F Y: F X: T W: F V: F Z: F Y: F X: F W: F V: F Z: T Y: T X: T W: T V: T None—the argument is valid. Z: T Y: T X: F W: F V: F 3 points Question 32 Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? S R ~D S D ~R S: F R: F D: F S: T R: T D: F S: F R: T D: F None—the argument is valid. S: T R: T D: T 3 points Question 33 Use a short form truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? (B • C) F (F • E) (J • P) (B • C) P B: F C: T F: T E: F J: F P: F B: T C: T F: T E: F J: T P: F None—the argument is valid. B: F C: F F: F E: F J: F P: F B: T C: T F: T E: T J: T P: F 3 points Question 34 Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? A B A ~B A: T B: T A: F B: F A: F B: T None—the argument is valid. A: T B: F 3 points Question 35 Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? ~(P • I) ~P ~I P: T I: F P: F I: F None—the argument is valid. P: T I: T P: F I: T 3 points Question 36 Use a truth table to answer the following question. Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? C • E E • C C: T E: T C: F E: F C: F E: T None—the argument is valid. C: T E: F 3 points Question 37 Which rule is used in the following inference? (D ~E) F F (G • H) (D ~E) (G • H) MT DD HS CD MP 3 points Question 38 Which rule is used in the following inference? (A • B) (C D) A • B C D HS DD CD MT MP 3 points Question 39 Which rule is used in the following inference? [(A B) (C B)] ~(~A • ~C) (A B) (C B) ~(~A • ~C) MP MT HS DD CD 3 points Question 40 Which rule is used in the following inference? ~(F • K) (F L) ~(F L) ~~(F • K) CD MP MT HS DD 3 points Question 41 Which rule is used in the following inference? (B • C) D ~D B • C Conj Add Simp HS DS 3 points Question 42 Which rule is used in the following inference? F G ~A (F G) Add Simp HS DS Conj 3 points Question 43 Which rule is used in the following inference? L • ~F ~F Conj DS HS Add Simp 3 points Question 44 Which rule is used in the following inference? E • (F G) H (F • G) [E • (F G)] • [H (F • G)] Conj DS HS Simp Add 3 points Question 45 Which rule is used in the following inference? ~(R S) [~O • (P Q )] ~(R S) [~O • (~~P Q )] DN Assoc Com Dist Taut 3 points Question 46 Which rule is used in the following inference? (M N) (~L • K) [(M N) ~L] • [(M N) K] Dist Assoc Taut Com DN 3 points Question 47 Which rule is used in the following inference? M M N Conj DS HS Simp Add 3 points Question 48 Which, if any, of the following proofs are correct demonstrations of the validity of this argument? (P • Q ) • (R S) Q Proof 1 (1) (P • Q ) • (R S) /Q Premise/Conclusion (2) P • Q 1 Simp (3) R S 1 Simp (4) P 2 Simp (5) Q 2 Simp Proof 2 (1) (P • Q ) • (R S) /Q Premise/Conclusion (2) P • Q 1 Simp (3) Q 2 Simp Proof 2 Proof 1 Proofs 1 and 2 Neither proof Not enough information is provided because proofs are incomplete. 3 points Question 49 Which, if any, of the following proofs are correct demonstrations of the validity of this argument? (P R) C C ~R Proof 1 (1) (P R) C /C ~R Premise/Conclusion (2) ~(P R) C 1 Imp (3) (~P • ~R) C 2 DM (4) C (~P • ~R) 3 Com (5) (C ~P) • (C ~R) 4 Dist (6) C ~R 5 Simp Proof 2 (1) (P R) C /C ~R Premise/Conclusion (2) ~(P R) C 1 Imp (3) (~P • ~R) C 2 DM (4) (~P C) • (~R C) 3 Dist (5) ~R C 4 Simp (6) C ~R 5 Com Proof 1 Proofs 1 and 2 Proof 2 Not enough information is provided because proofs are incomplete. Neither proof 3 points Question 50 Which, if any, of the following proofs are correct demonstrations of the validity of this argument? A (B C) B (~C ~A) Proof 1 (1) A (B C) /B (~C ~A) Premise/Conclusion (2) (A • B) C 1 Exp (3) (B • A) C 2 Com (4) B (A C) 3 Exp (5) B (~C ~A) 4 Contra Proof 2 (1) A (B C) /B (~C ~A) Premise/Conclusion (2) B Assumption (3) A Assumption (4) B C 1, 3 MP (5) C 2, 4 MP (6) A C 3–5 CP (7) B (A C) 2–6 CP (8) B (~C ~A) 7 Contra Proofs 1 and 2 Proof 1 Neither proof Proof 2 Not enough information is provided because proofs are incomplete. 3 points

Explanation / Answer

* Tautology. As it is true and remains true under every assignment of truth values to its individual letters.

*coherency

* "~" is used for this purpose.

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