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**The following questions were taken from old tests. They are provided as a source of extra practice and are just a SAMPLE of possible types of test questions. You must still study ALL the material covered from your homework assignments, class notes & review as you study & prepare for the test. Go to the Math Lab if you have any problems with the material. Note: Just because a topic does not appear here does NOT mean it will not be on your test. Answers are listed at the end. 1) Write in roster form the set E that contains the natural numbers between six and thirteen. 2) Express set A = { 4, 5, 6, 7, 8, 9 } in set builder notation. 3) Which of these sets are NOT well-defined: I. The set of the ten most famous movie stars. II. The set of colors in the US flag. III. IV. The set of coin denominations currently being minted in the US. The set of the five best tasting ice cream flavors. a) I and IV only b) none of them c) I, II and III only d) all of them e) II and III only 4) If A = **

6 15

** ; find n ( A ) 5) For sets A & B determine if **

*A*

*A*

** A = **

{

*B*

14

19 }

**6) How many proper subsets does {q, w, e, r, t, y} have ? 7) True or False: a) **

*p*

*e n p*

**b)**

*p*

{ , , }

**c)**

** {0} d) A **

** A **

**= **

** e) If n (A **

** B) = 0, then A & B are disjoint sets.**

**8a) List all the subsets of { a, g, n } b) List one set that is equivalent to this set. 9) Given U = { 0,1,2,3,4, …,12} ; A = { 3,5,7,9,10 } ; B = { 2,3,4,7,9,11} Find: a) **

*B*

** b) **

*A*

*B*

** c) **

*A*

*B*

** d) **

*A*

*B*

*B*

**10) Given**

:

**U={16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27} ; A={19, 21, 23, 25, 27} ; B={24, 25, 26, 27} Find:**

*A*

'

*B*

'

**11) Set M contains 33 elements, set P contains 46 elements, and 10 elements are common to both sets. Determine **

*P*

**12) Use Venn diagram regions to determine if **

*A*

*B*

*A*

*B*

** for all sets A and B. ANSWERS: 1) E = {7,8,9,10,11,12} 2) A = **

{

3 10}

** 3) a 4) 9 5) **

*A*

*B*

** 6) 63 7a) TRUE b) FALSE c) FALSE d) FALSE e) TRUE 8a) { }, {a}, {g}, {n}, {a,g}, {a,n}, {g, n}, {a,g,n} 8b) Any 3 element set 9a) { 0,1, 5,6,8,10,12 } b) { 2,3,4,5,7,9,10,11 } c) { 5,10} d) { 0,1,5,6,8,10,12 } 10) { 16,17,18,19,20,21,22,23,24,26} 11) 69 12) yes – they are equal – see the text for the work using set regions 1 through 4 **