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1. Use a truth tabte to determine whether (p → q) → r and p ∧ K (q ∨ ~ r) are equivalent.
2. Use a truth tabte to determine whether the argument form is valid.
~ p
q
∴ p → q
3. Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except for one. He deduced who killed Sharky on the basis of the following statements:
(a) Socko: Lefty killed Sharky.(b) Fats: Muscles didn‘t kill Sharky.(c) Lefty: Muscles was shooting craps with Socko when Sharky was knocked off.(d) Muscles: Lefty didn‘t kill Sharky.
Who did kill Sharky?
4. Given any integers a, b, and s, if a - b is odd and b - s is even, what can you say about the parity of a - s? Prove your answer.
5. Prove that for all real numbers r, if r2 is irrational, then r is irrational.
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Question 1 and 2 are examples of basic truth table. Question 3 is application of truth table in solving practical problems. Question 4 and 5 are from basic number system. All problems are solved in a detailed manner. Studying the assignment you will understand how to solve this kind of problems on your own.
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MATH 3070 Lab Project - Find a 90% confidence interval for the differences of mean. What do you assume about the data? In particular, are the two samples independent and Find a 90% confidence interval for the differences of the means. What do you as..
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Let T ⊂ R3 denote the doughnut-shaped surface obtained by revolving the circle (y - 2)2 + z2 = 1 around the z-axis. Give T the orientation determined by the outward unit normal. Compute the surface area of T
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