Counts Double

Let A be the set of all students who enjoy solving puzzles

Let B be the set of all students who do well in IST 230

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Now use the following “facts” to give a formal proof that A = B (Hint: remember you must prove two separate things). The “facts” are:

(1) If a student is a good problem solver, then the student does well in IST 230

(2) If a student enjoys solving puzzles, then the student is a good problem solver

(3) If a student does well in IST 230, then the student is a good problem solver

(4) If a student is a good problem solver, then the student enjoys solving puzzles

2. Give the definition and a concrete example of a proper subset

3. Let A be the set of all integers x such that x is = k² for some integer k

Let B be the set of all integers x such that the square root of x, SQRT(x), is an integer

Give a formal proof that A = B. Remember you must prove two things: (1) if x is in A, then x is in B, AND (2) if x is in B, then x is in A

4. Explain when two sets are disjoint and give a concrete example

Tell whether or not the following are equal. Explain your answers. HINT: look carefully at the notations used

5. {1, 2, 1, 3} = {3, 2, 1}

6. (1, 2, 1, 3) = (3, 2, 1)

7. (1, 2, 1, 3) = (1, 2, 3, 1)

Let A = {5, 6} B = {g, h, i} C = {a, b}

8. Calculate A x B x C =

Let A = {1, 2, x} B = {d, e, f} C = {2, x, y} U = {1, 2, d, e, f, x, y}

9. Calculate A ? C =

10. Calculate A ? B =

11. Calculate A – C =

12. Calculate C^C (the set complement of C) =

13. Give an example of a partition of set U