Philosophy logic

There are 8 questions. Please complete them perfectly. I need good grades.

The questions in the file”problem 2″

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The other document is last week’s homework, which can be completed according to the scale corrected by the professor.

• Are the following schemata valid?Justify your answers.
• (p ⊃ q) ⊃ (p ⊃ q.r)(b) (p ⊃ q) ⊃ (p ⊃ q∨r)
• Does schema (i) imply schema (ii)? Does schema (ii) imply schema (i)?
• In the following, determine whether the first schema implies the second.Justify your answers.
• (p⊃r) ≡(q⊃r)p ≡ q (b) (r⊃p) ≡ (r⊃q)p ≡ q
• Without using truth-tables, show that

(c) (p ≡ q) ∨ (p ≡ r) ∨ (q ≡ r)

Justify your answers.

(i) (p ≡ q.r) ⊃ -(p.q)(ii) (p ⊃ q.r) ≡ -(p.q)

(c) p≡ q.r p ⊃ (q≡ r)

(1) the conjunction of “q.(r ∨ s.t) ⊃ u” and “u∨-r⊃p”implies(2) “q⊃p∨s”.(We’ll allow “u” to count as a sentence letter here.)

Proceed as follows. Start by considering what must be the case for any interpretation making schema (2) false.Then argue that any such interpretation must therefore make schema (1) false as well.

• Consider the following two sentences:
• For the following arguments, determine whether the premises truth-functionally imply the conclusion.

(i)If your prices are low then your sales will be high, and if you sell quality merchandise then your customers will be satisfied.

(ii)If either your prices are low or you sell quality merchandise, then either your sales will be high or your customers satisfied.

Show that sentence (i) truth-functionally implies sentence (ii), but that (ii) does not truth-functionally imply (i).

You should proceed by schematizing the premises and conclusion of the argument, saying what your sentence letters stand for.Then show that the implication holds between the corresponding schemata, or show that it doesn’t.

(a)Either productivity will rise and the stock market will recover, or productivity won’t rise but inflation will moderate, or inflation won’t moderate and the stock market will not recover. (PREMISE 1)

If productivity rises then inflation will moderate. (PREMISE 2)

THEREFORE, the stock market will recover provided that productivity rises. (CONCLUSION)

(b)If Smith wasn’t the murderer and Jones wasn’t lying, then Jones met Smith last night. (PREMISE 1)

If Jones met Smith last night or the murder did not take place after midnight, then Smith was the murderer.(PREMISE 2) If Smith wasn’t the murderer and Jones was lying, then the murder did not take place after midnight. (PREMISE3) THEREFORE, Smith was the murderer. (CONCLUSION)

• Consider the following two sentences:
• For the following arguments, determine whether the premises truth-functionally imply the conclusion.

(i)If your prices are low then your sales will be high, and if you sell quality merchandise then your customers will be satisfied.

(ii)If either your prices are low or you sell quality merchandise, then either your sales will be high or your customers satisfied.

Show that sentence (i) truth-functionally implies sentence (ii), but that (ii) does not truth-functionally imply (i).

You should proceed by schematizing the premises and conclusion of the argument, saying what your sentence letters stand for.Then show that the implication holds between the corresponding schemata, or show that it doesn’t.

(a)Either productivity will rise and the stock market will recover, or productivity won’t rise but inflation will moderate, or inflation won’t moderate and the stock market will not recover. (PREMISE 1)

If productivity rises then inflation will moderate. (PREMISE 2)

THEREFORE, the stock market will recover provided that productivity rises. (CONCLUSION)

(b)If Smith wasn’t the murderer and Jones wasn’t lying, then Jones met Smith last night. (PREMISE 1)

If Jones met Smith last night or the murder did not take place after midnight, then Smith was the murderer.(PREMISE 2) If Smith wasn’t the murderer and Jones was lying, then the murder did not take place after midnight. (PREMISE3) THEREFORE, Smith was the murderer. (CONCLUSION)

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