Lecture Notes for MATH 302 - DISCRETE MATHEMATICS at Texas A&M (A&M)

Notes Information

Material Type:Review Sheet
University:Texas A&M University
  • Proposition
  • Contrapositive
  • Contingency
  • Contradiction
  • Rational Number
  • Differentiable Function
  • Differentiable
  • Following Pairs
  • Nonempty Set
  • Composition
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MATH 302.903 Practice Problems for Examination 1 Spring 2006 1. For each of the following sentences, indicate whether it is a proposition, and in the case that it is a proposition also indicate its truth value. (a) 7 divides 13n ?1. (b) A function f : R ? R is differentiable if and only if f(0) is a rational number. (c) For every even integer n, 12n3 ?2n2 + 18 is even. (d) ? ? ?. (e) ? ? A. (f) f(x) is of order ex. (g) floorleftpifloorright = 3. 2. Let n and m be positive integers. Consider the following proposition P: "If n and m are both divisible by 3 then n(m + 1) is even." Write the converse, inverse, and contrapositive of P. 3. Incorporate each of the following sentences into a false proposition. (a) ? ? A. (b) f is bounded. (c) |A| = 8. (d) Every differentiable function f : R ? R is continuous. (e) A ? (B ?C). 4. Determine, with proof, the least integer n such that x4 lnx?3x2 + 4 is O(xn). 1 5. Determine which of the following pairs of compound propositions are logically equiva- ...

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