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social science
introduction to logic

Questions and Answers of Introduction To Logic

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
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
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
Use truth tables to decide which of the following biconditionals are tautologies.p = [p ꓦ (q ꓦ ~ q)]
Use indirect proof to prove that the following statements are tautologies.(A ⊃ B) ꓦ (~ A ⊃ B)
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.(W ⊃ X) ⊃ [(X ⊃ Y) ⊃ (W ⊃ Y)]
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
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,
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
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If there is a single norm for greatness
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.(A ⊃ B) ꓦ (B ⊃A)
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[(W ⊃ X) ⋅ (W ⊃ Y)] ⊃ [W ⊃ (W ꓦ Y)]
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
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,
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
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
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
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If the butler were present, he would
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.(A ⊃ B) ꓦ (B ⊃C)
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[(W ⊃ X) ⋅ (W ⊃ Y)] ⊃ [W ⊃ (W ⋅ Y)]
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
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,
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
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
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
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If the butler told the truth, then the
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.(A ⊃ B) ꓦ (~ A ⊃ C)
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.(W ⊃ X) ⊃ [W ⊃ (W ⋅ 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,
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
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
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
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
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.Their chief would leave the country if
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.A ꓦ (A ⊃ B)
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.(W ⊃ X) ⊃ [(~ W ⊃ 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,
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
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
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
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
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
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If the investigators of extrasensory
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.R ≡ ~~ R
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.(W ⊃ X) ⊃ [(W ⋅ Y) ⊃ (X ⋅ Y)]
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
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,
For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If we buy a lot, then we will build a
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.G ≡ [G ⋅ (G ꓦ H)]
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[(W ⊃ X) ⊃ X] ⊃ (W ꓦ X)
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case making the formula begin with a quantifier, not with a negation symbol.Nothing is
For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If your prices are low, then your sales
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.G ≡ [G ꓦ (G ⋅ H)]
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.(G ⊃ H) ⊃ [(F ꓦ G) ⊃ (H ꓦ F)]
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case making the formula begin with a quantifier, not with a negation symbol.No one
For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If your prices are low, then your sales
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.~ [(D ⊃ ~ D) ⋅ (~ D ⊃ D)]
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[A ⊃ (B ⋅ C)] ⊃ {[B ⊃ (D ⋅ E)] ⊃ (A . D)}
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case making the formula begin with a quantifier, not with a negation symbol.He only earns
For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If Jordan joins the alliance, then
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
Use indirect proof to prove that the following statements are tautologies.(Q ⊃ R) ≡ [~ R ⊃ ~ Q)]
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[(A ꓦ B) ⊃ C] . {[C ꓦ D) ⊃ E] ⊃ (A ⊃ E)}
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case making the formula begin with a quantifier, not with a negation symbol.No man is
If we replace statement variables p, q, r and s in the foregoing argument form with simple statements T, U, V and W, respectively, we get the following argument.(P1): T ⊃ (U ⋅ V)(P2): (U ꓦ V)
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If either Jordan or Algeria joins the
Use indirect proof to prove that the following statements are tautologies.(Q ⊃ R) ⊃ [(P ⊃ Q) ⊃ (P ⊃ R)]32
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[(A ⊃ B) ⊃ A] ⊃ A
For each of the following arguments, a formal proof of validity can be constructed without great difficulty, although some of the proofs may require a sequence of eight or nine statements (including
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case making the formula begin with a quantifier, not with a negation symbol.Not
Identify the kinds of agreement or disagreement most probably exhibited by the following pairs:a. A bad peace is even worse than war.—Tacitus, Annalsb. The most disadvantageous peace is better than
Each of the following arguments in English may be similarly translated, and for each, a formal proof of validity (using only the nine elementary valid argument forms as rules of inference) may be
For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments.In these formal

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