Math 225 - Vocabulary and Concepts (5.1, 5.2)

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Across
  1. 2. / for any non-negative integer n, _______ is a set of n elements
  2. 5. / the number of r-combinations of an n-set (Challenge: after you fill in the vocabulary term, write out the associated equation on the side of your paper)
  3. 6. / the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those of graph theory
  4. 7. / mathematically, if S = "If A, then B", then this is "If not B, then not A"
  5. 10. / right hand side
  6. 13. Principle / (two words) if we are given a counting problem with can be broken down into three successive stages with A outcomes in the first stage, B in the second, and C in the third, and if the composite outcomes are all distinct, then the total number of outcomes is A * B * C
  7. 17. / a counting problem can be broken into _______ if the problem can be solved in some number of successive steps
  8. 18. / mathematically, if S = "If A, then B", then this is "If B, then A"
  9. 19. / the number of ways to make a selection if order doesn't matter (i.e. selections)
  10. 20. / a counting problem can be broken into _______ if the problem if each set of possible solutions to the problem are disjoint (i.e. no overlap between solution sets)
  11. 21. / for any non-negative integer r, _______ is an ordered arrangement of r elements taken from a set S
  12. 22. / this is a type of error that occurs in solving counting problems when the number possible permutations is calculated rather than the number of combinations
Down
  1. 1. / left hand side
  2. 3. / a type of problem where you are given a grid of squares and a particular tile (e.g. a domino) and asked to determine whether it is possible to cover the grid with no overlaps using tiles of the given shape and size
  3. 4. / the number of r-permutations of an n-set (Challenge: after you fill in the vocabulary term, write out the associated equation on the side of your paper)
  4. 6. / to show that a statement is false, you can provide one of these
  5. 7. / a statement that follows with little or no proof required from an already proven statement (i.e. a consequence of a theorem)
  6. 8. / the number of ways to put things in order (i.e. arrangements)
  7. 9. Principle / (two words) if we are given three disjoint sets with A, B, and C elements in each set, then there are A + B + C ways to choose an element from one of the sets
  8. 11. / in a grid, when two squares (of the same size) share an edge
  9. 12. / for any non-negative integer r, _______ is a set of r-elements from a set S
  10. 14. / a type of conditional statement written in two parts: a hypothesis and a conclusion
  11. 15. / when the intersection of two sets A and B is empty, then the sets are...
  12. 16. / a subsidiary or intermediate theorem in an argument or proof (i.e. a side effect of a proof)