C241 PLTL SESSION – 2/24/2015 Set Theory & Functions.

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C241 PLTL SESSION – 2/24/2015 Set Theory & Functions

Warm-Up Exercise Grab a worksheet Begin completing the worksheet in pairs or small groups

Problem 1 a. Give, in set builder notation, the set of all even numbers. b. Give, in set builder notation, the set of all odd numbers. c. Give, in set builder notation, the set of all irrational numbers. d. A Mersenne prime is given by the equation 2^p – 1, where p is a prime number. If P is the set of all primes, give the set of all Mersenne primes in set builder notation.

Problem 2 In your own words, define the following terms: a. One-to-one (a.k.a. injection) b. Onto (a.k.a. surjection) c. Bijection (a.k.a. one-to-one correspondence)

Problem 3 Classify the following functions as injective, surjective, or bijective: (Assume that each function is f: R  R unless otherwise indicated) a. f(x) = x^2 b. f(x) = x^0.5 c. f: Z  {0,1} f(x) = x mod 2