m325pracfin - M325K Practice Mega-Final 1 Make a truth...

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M325K Practice Mega-Final 1. Make a truth table for the statement q ( p q ) . 2. Write the negation of “My computer is broken or I’m doing something wrong.” 3. Write the contrapositive of “If I’m doing things correctly, then my computer is not broken.” 4. Exercise 41 on page 63. 5. Let A be a finite set. Use the strong form of mathematical induction to prove that |P ( A ) | = 2 | A | . 6. Translate the following statement into logical symbols and use your expression to write a good English negation of it. “Every student in this class has an ancestor from Texas.” 7. Prove or disprove: If n is odd, then n 2 is odd. 8. Prove by contradiction: If 3 n + 2 is odd, then n is odd. 9. Prove or disprove: For every prime number n , n + 2 is prime. 10. Prove or disprove that for all positive integers n , 1 · 1! + 2 · 2! + 3 · 3! + · · · + n · n ! = ( n + 1)! - 1 . 11. Prove the generalization of DeMorgan’s Law: For sets
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  • Spring '08
  • SCHURLE
  • Math, Natural number, relation equivalence relation, good English negation, statement tautology contradiction, disjoint partition power, proper subset complement

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