Math 225 - Vocabulary and Concepts (5.1, 5.2)

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Across
  1. 4. for any non-negative integer r, ______ is a set of r-elements from a set S
  2. 7. for any non-negative integer r, ______ is an ordered arrangement of r elements taken from a set S
  3. 8. right hand side
  4. 10. 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)
  5. 11. a counting problem can be broken into ______ if the problem can be solved in some number of successive steps
  6. 12. mathematically, if S = "If A, then B", then this is "If B, then A"
  7. 17. a counting problem can be broken into ______ if each set of possible solutions to the problem are disjoint (i.e. no overlap between solution sets)
  8. 18. (two words, no space) if we are given a counting problem which can be broken 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
  9. 19. in a grid, when two squares (of the same size) share an edge
  10. 21. the number of ways to make a selection if order doesn't matter (i.e. selections)
  11. 22. left hand side
Down
  1. 1. (two words, no space) 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
  2. 2. a subsidiary or intermediate theorem in an argument or proof (i.e. a side effect of a proof)
  3. 3. the number of ways to put things in order (i.e. arrangements)
  4. 5. to show that a statement is false, you can provide one of these
  5. 6. for any non-negative integer n, ______ is a set of n elements
  6. 9. this is a type of error that occurs in solving counting problems when the number of possible permutations is calculated rather than the number of combinations
  7. 13. mathematically, if S = "If A, then B", then this is "If not B, then not A"
  8. 14. a type of conditional statement written in two parts: a hypothesis and a conclusion
  9. 15. when the intersection of two sets A and B is empty, then the sets are ______
  10. 16. the branch of mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those in graph theory
  11. 20. 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)
  12. 21. a statement that follows with little or no proof required from an already proven statement (i.e. a consequence of a theorem)