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social science
introduction to logic
Introduction To Logic 15th Edition Irving M. Copi, Carl Cohen, Victor Rodych - Solutions
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[D ⊃ (F ⊃ G)] ⊃ [(D ⊃ F) ⊃ (D ⊃ G)]
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): A ⊃ (B ⋅ C)(P2): B ⊃ (D ⋅ E)(P3): (A ⊃ D) ⊃ (F ≡ G)(P4): A ⊃ (B ⊃ ~ F)(P5): ~ F ⊃ (~ G ⊃ E)∴ E
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): (I ≡ H) ⊃ ~ (H
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (I ꓦ ~~ J) ⋅ K2. [~ L ⊃ ~ (K ⋅ J)] ⋅[K ⊃ (I ⊃ ~ M)]∴ ~ (M ⋅ ~ L)3. [(K ⋅ J) ⊃ L] ⋅[K ⊃ (I ⊃ ~ M)]4. [(K ⋅ J) ⊃ L] ⋅[(K ⋅
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): [C ⋅ (D ⋅ ~ E)] ⋅ [(C ⋅ D) ⋅ ~ E]∴
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. (L ⊃ M) ⊃ (N ≡ O)2. (P ⊃ ~ Q) ⊃ (M ≡ ~ Q)3. {[(P ⊃ ~ Q) ꓦ (R
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.G ⊃ (H ⊃ G)
If there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.~ (A ⋅ C)T
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): T ⊃ (U ⋅ V)(P2): U ⊃ (W ⋅ X)(P3): (T ⊃ W) ⊃ (Y ≡ Z)(P4): (T ⊃ U) ⊃ ~ Y(P5): ~ Y ⊃ (~ Z ⊃ X)∴ X
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.Snake bites are sometimes fatal. ( Sx: x is a snake bite; Fx: x is fatal.)
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): (F ≡ G) ⊃ ~ (G
Use Conditional Proof to prove the validity of the following arguments. G (P₁): (HD) (P₂): (CD) (E > F) (P₂): G (CVE) (P): (DVF) (HVD) :. G = (DVF)
For each of the following arguments, construct an indirect proof of validity. P₁: B [(OV~0) (TVU)] P₂: UD~(GV-G) 2 :. BOT
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): Z ⊃ (A ⊃ B)∴ Z ⊃ (~~ A ⊃ B)
For each of the following arguments, construct an indirect proof of validity. P₁: (FVG) (D. E) P₂: (EVH) DQ 2° P₂: (FVH) ::Q
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.~
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (D ⋅ E) ⊃ ~ F2. F ꓦ (G ⋅ H)3. D ≡ E∴ D ⊃ G4. (D ⊃ E) ⋅ (E⊃ D)5. D ⊃ E6. D ⊃ (D ⋅ E)7. D ⊃ ~ F8. (F ꓦ G) ⋅ (F ꓦ H)9. F ꓦ
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. I ⊃ J2. I ꓦ (~~ K ⋅ ~~ J)3. L ⊃ ~ K4. ~ (I ⋅ J)∴ ~ L ꓦ ~
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): (O ⋅ P) ⊃ (Q ⊃ R)(P2): S ⊃ ~ R(P3): ~ (P ⊃ ~ S)(P4): ~ (O ⊃ Q)∴ ~ O
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.Only licensed physicians can charge for medical treatment. (Lx: x is a
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
Use Conditional Proof to prove the validity of the following arguments. (P₁): [W] (~X~Y)] · [ZƆ ~ (XVY)] (P₂): (~AW) (~BZ) (P3): (AX) (BY) :. X = Y +
Use Conditional Proof to prove the validity of the following arguments. (P₁): (KL) (P₂): (LVN) :. K = M (MN) {[O (OVP)] (K.M)}
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): (B ⋅ C) ⊃ (D
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.A
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. A ⊃ B2. B ⊃ C3. C ⊃ A4. A ⊃ ~ C∴ ~ A ⋅ ~ C5. A ⊃ C6. (A ⊃ C) ⋅ (C ⊃ A)7. A ≡ C8. (A ⋅ C) ꓦ (~ A ⋅ ~ C)9. ~ A ꓦ ~ C10. ~ (A ⋅
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): (X ꓦ Y) ⋅ (~ X ꓦ ~ Y)∴ [(X ꓦ Y) ⋅ ~
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. F ⊃ ~ G2. ~ F ⊃ (H ⊃ ~ G)3. (~ I ꓦ ~ H) ⊃ ~~ G4. ~ I∴ ~ H5. ~ I
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.No boy scout ever cheats. ( Bx: x is a boy scout; Cx: x cheats.)
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
For each of the following arguments, construct an indirect proof of validity. P: (OVP) P₂: (EVL) P3: (QVZ) ::~0 (D. E) (QV~D) - (O. E)
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): (J ⋅ K) ⊃ (L ⊃ M)(P2): N ⊃ ∼ M(P3): ~ (K ⊃ ∼ N)(P4): ∼ (J ⊃ ~ L)∴ ~ J
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.G
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): (S ≡ T) ꓦ [(U
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. Y ⊃ Z2. Z ⊃ [Y ⊃ (R ꓦ S)]3. R ≡ S4. ~ (R ⋅ S)∴ ~ Y5. (R ⋅ S) ꓦ (~ R ⋅ ~ S)6. ~ R ⋅ ~ S7. ~ (R ꓦ S)8. Y ⊃ [Y ⊃ (R ꓦ
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): (T ꓦ ~ U) ⋅ [(W ⋅ ~ V) ⊃ ~ T]∴ (T ꓦ ~
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. (A ꓦ B) ⊃ C2. (C ꓦ B) ⊃ [A . (D ≡ E)]3. A ⋅ D∴ D ≡ E4. A5. A
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.“To swim is to be a penguin.” ( Sx: x swims; Px: x is a
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): [(D ꓦ E) ⋅ F] ⊃ G(P2): (F ⊃ G) ⊃ (H ⊃ I)(P3): H∴ D ⊃ I
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. T ⋅ (U ꓦ V)2. T ⊃ [U ⊃ (W ⋅ X)]3. (T ⋅ V) ⊃ ~ (W ꓦ X) ∴ W ≡ X4. (T ⋅ U) ⊃ (W ⋅ X)5. (T ⋅ V) ⊃ (~ W ⋅ ~ X)6. [(T ⋅ U) ⊃ (W
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): ~ (R ꓦ S) ⊃ (~ R ꓦ ~ S)∴ (~ R ⋅ ~ S)
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. W ⊃ X2. (W ⊃ Y) ⊃ (Z ꓦ X)3. (W ⋅ X) ⊃ Y4. ~ Z∴ X5. W ⊃ (W ⋅
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. Q ⊃ R2. ~ S ⊃ (T ⊃ U)3. S ꓦ (Q ꓦ T)4. ~ S∴ R ꓦ U5. T ⊃ U6. (Q
For each of the following arguments, construct an indirect proof of validity. P₁: DD (ZDY) P₁: ZD (Y-Z) 2° ::~DV~Z)
Use Conditional Proof to prove the validity of the following arguments. (P₁): QV (RS) (P₂): [R (RS)] - (TV U) (UV) (P₂): (TQ) :. QVV .
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.H
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.Diplomats are not always rich. ( Dx: x is a diplomat; Rx: x is rich.)
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): [(X ⋅ Y) ⋅ Z] ⊃ A(P2): (Z ⊃ A) ⊃ (B ⊃ C)(P3): B∴ X ⊃ C
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of ways that, the statement can be true (or false), as the case requires.G
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): [N ⊃ (O ⋅ P)]
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (Q ꓦ ~ R) ꓦ S2. ~ Q ꓦ (R ⊃ ~ Q)∴ R ⊃ S3. (~ Q ꓦ R) ⋅ (~ Q ꓦ ~ Q)4. (~ Q ꓦ ~ Q) ⋅ (~ Q ꓦ R)5. ~ Q ꓦ ~ Q6. ~ Q7. Q ꓦ (~ R ꓦ S)8. ~
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first two in the exercise set immediately following.(P1): O ⊃ [(P ⊃ Q) ⋅ (Q ⊃ P)]∴ O ⊃ (P ≡ Q)
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. N ⊃ O2. (N ⋅ O) ⊃ P3. ~ (N ⋅ P)∴ ~ N4. N ⊃ (N ⋅ O)5. N ⊃ P6. N
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier, not with a negation symbol.Sparrows are not mammals. (Sx: x is a sparrow; Mx: x is a mammal.)
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your command of the rules of inference, a needed preparation for the construction of proofs that are
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that is not a premise).1. A ⋅ B2. (A ꓦ C) ⊃ D∴ A ⋅ D3. A4. A ꓦ C5. D6. A ⋅ D
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the rule of inference by which its conclusion follows from its premise or premises.(P1): (A · B) р ⊃
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya raises the price of oil,” and “Saudi Arabia buys five hundred more warplanes,” symbolize these
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true? ~ {~[(B · ~ C) ꓦ (Y · ~ Z)] · [(~ B ꓦ X) ꓦ (B ꓦ ~Y )]}
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~ {[(~ A ⋅ B) ⋅ (~ X ⋅ Z)] ⋅ ~ [(A ⋅ ~ B) ꓦ ~ (~ Y · ~ Z)]}
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[A · (B ꓦ C)] · ~[(A · B ) ꓦ (A · C)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[X ꓦ (Y · Z)] ꓦ ~[(X ꓦ Y) · (X ꓦ Z)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[A ꓦ (B ꓦ C)] · ~[(A ꓦ B) ꓦ C]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~[(A ⋅ B) ꓦ ~(B ⋅ A)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(A ꓦ C)ꓦ ~ (X · ~Y)
Use truth tables to decide which of the following biconditionals are tautologies.[(p ⊃ q) · (q ⊃ p)] ≡ [(p · q) ꓦ (~ p · ~ q)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(X V Z) · (~ X V Z)
Symbolize the following, using capital letters to abbreviate the simple statements involved.Chile will call for a meeting of all the Latin American states only if both Argentina mobilizes and Brazil protests to the UN.
Use truth tables to decide which of the following biconditionals are tautologies.[(p · q) ⊃ r] = [p ⊃ (q ⊃ r)]
Symbolize the following, using capital letters to abbreviate the simple statements involved.Brazil will protest to the UN only if Argentina mobilizes.
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(A ꓦ Y) · (B ꓦ X)
Use truth tables to decide which of the following biconditionals are tautologies.[p ꓦ (q · r)] = [(p ꓦ q) · (p ꓦ r)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?(X ꓦ Y) · (X ꓦ Z)
Symbolize the following, using capital letters to abbreviate the simple statements involved.Brazil will protest to the UN if Argentina mobilizes.
Use truth tables to decide which of the following biconditionals are tautologies.[p ꓦ (q · r )] = [(p ⋅ q) ꓦ (p ⋅ r)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?(B ꓦ C) · (Y ꓦ Z)
Symbolize the following, using capital letters to abbreviate the simple statements involved.If it is not the case that Argentina mobilizes, then Brazil will not protest to the UN, and Chile will call for a meeting of all the Latin American states.
Use truth tables to decide which of the following biconditionals are tautologies.[p · (q ꓦ r)] = [(p ꓦ q) · (p ꓦ r)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?(A ꓦ X) · (Y ꓦ B)
Symbolize the following, using capital letters to abbreviate the simple statements involved.It is not the case that if Argentina mobilizes, then both Brazil will protest to the UN, and Chile will call for a meeting of all the Latin American states.
Use truth tables to decide which of the following biconditionals are tautologies.[p · (q ꓦ r)] = [(p ⋅ q) ⋅ ( p ⋅ r)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(X · ~Y) ꓦ (B · ~C)
Symbolize the following, using capital letters to abbreviate the simple statements involved.If Argentina does not mobilize, then neither will Brazil protest to the UN nor will Chile call for a meeting of all the Latin American states.
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