Homework 1

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1. Write a formal description for each of the following sets
   1. The set containing all integers which are multiples of 3 and are larger than 17.
   2. The set containing all integers which have either 2 or 3 (or both) as a factor.
2. Let A = {1,2,3,4}, and B = {X,Y,Z}.
   1. List the elements of A×B
   2. List the elements of B×A
   3. What is |P(A×B)|?
3. Use induction to prove that 2⁰ + 2¹ + 2² + ... + 2^k = 2^k+1-1 for k > 0.
4. Prove that congruence modulo n is an equivalence relation on the set of integers.