Solutions to Review Test1

 

  1. The hypothesis and the conclusion are both parts of a conditional statement. The hypothesis is found after IF and the conclusion is found after THEN.
  2. DECISION: The cat is not blue. The statements follow logic rule B, which rejects/denies the conclusion and that tells us that the hypothesis is not true.
  3. a. 57, 72  arithmetic sequence with a common difference of 15

b. 96, 192 geometric sequence with a common ratio of 2

  1. Sets are equal when they have exactly the same elements in them; the elements can be in a different order, however. Sets are equivalent when they have the same number of elements or a 1-1 correspondence. Sets are disjoint when they have nothing in common.
  2. a. two separate circles     b.  two or more circles shaded the same     c. rectangle    d.  circle within a circle  e.  two overlapping circles with the same shading
  3. {A, B, 1, 2}, {A}, {B}, {1}, {2}, {A, B}, {A, 1}, {A, 2}, {B, 1}, {B, 2}, {1, 2}, {A, B, 1}, {A, B, 2}, {A, 1, 2}, {B, 1, 2}, F
  4. a.  never     b.  always     c.  sometimes
  5. It takes two statements to be equivalent: If A, then B. and If B, then A.
  6. a. {pencil}  b.  {paper, book, pencil, pen, crayon, lipstick}  c.  {paper, book, pencil} = M
  7.  concrete, semi-concrete, abstract
  8. The solution is the methods or processes we use to obtain the answer. The answer is the resolution to the question/problem.
  9. INVERSE: If the set is not empty, then it has elements.

CONVERSE: If a set has no elements, then it is the empty set.

CONTRAPOSITIVE: If a set has elements, then it is not the empty set.

  1. Logic rule B denies the conclusion, which says the hypothesis is false. The decision is based on the situation stated in the conditional and would be the inverse of the hypothesis in the conditional.
  2. Logic rule A satisfies the hypothesis, which says the conclusion is true. The decision is based on the situation stated in the conditional and would be whatever the conclusion says in the conditional.
  3. JOINING describes/defines addition. The models commonly used are the union of disjoint sets, continuous lengths, and the number line with directed segments/distances.
  4. The original set must have 4 elements because 24 = 16 since we know the power of 2 is also the number of elements in the set.
  5.       a.  Commutative Property of Addition
    1. Closure
    2. Additive Identity
    3. Associative Property of Addition