- Select the contrapositive of: If it snows tonight, then I will stay at home.
Select the correct interpretations (may be more than one) of the notation
- Let
Q(x)
be the statement, "x - 1
". If the universe consists of all integers, what is the truth value of?
- Choose the prime numbers from the following list:
MAT 230 Quiz 1 MAT 230 Final Exam 1. Select the contrapositive of: If it snows tonight, then I will stay at home. a. If I stay at home, then it will snow tonight. b. If I do not stay at home, then it will not snow tonight. c. If it does not snow tonight, then I will not stay at home. d. none of the above. 2. Select the correct interpretations (may be more than one) of the notation ) ( x xP " a. P(x) is true for all x b. P(x) is true for at least one x c. There is no x for which P(x) is true d. There is an x such that P(x) is true 3. Let Q(x) be the statement, "x - 1 < 2x".="" if="" the="" universe="" consists="" of="" all="" integers,="" what="" is="" the="" truth="" value="" of="" )="" (="" x="" xq="" $="" a.="" true="" b.="" false="" 4.="" choose="" the="" prime="" numbers="" from="" the="" following="" list:="" a.="" 3="" b.="" 14="" c.="" 19="" d.="" 21="" 5.="" find="" the="" gcd(99,198).="" a.="" 3="" b.="" 9="" c.="" 33="" d.="" 99="" 6.="" solve="" the="" congruence:="" )="" 11="" (mod="" 5="" 2="" º="" x="" a.="" 5="" b.="" 6="" c.="" 7="" d.="" 8="" 7.="" fibonacci="" numbers="" are="" defined="" as:="" 2="" 1="" -="" -="" +="n" n="" n="" f="" f="" f="" for="" n=""> 1. The first six Fibonacci numbers are: 1, 2, 3, 5, 8, 13. What is the next Fibonacci number? a. 19 b. 21 c. 23 d. 25 8. Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and 3 2 ) 2 ( ) 1 ( ) ( - + - = n f n f n f for n > 1. a. 5 b. 25 c. 33 d. 1214 9. Find the sequence for the recursive formula: 9 1 + - = - n n s s , 3 0 - = s a. 14, -4, 14, -4 b. 6, 14, 86, 734 c. -3, 12, -3, 12 d. -3, 9, -3, 9 10. How many different license plates can be created with 7 numbers if any digit is allowed? a. 604,800 b. 10,000,000 c. 282,475,249 d. 823,543 11. Find the value of C(16, 6). a. 8,008 b. 924 c. 5,765,760 d. 12,870 12. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the department if at least one woman must be on the committee? a. 4242 b. 126 c. 931 d. 1131 13. True of False? 2 = n a is a solution to the recurrence relation 2 1 2 - - - = n n n a a a a. True b. False 14. If you deposit $10,000 in an account that yields 5% interest compounded yearly, what will be the balance at the end of 5 years? a. $12,625 b. $13,382 c. $12,763 d. $14,186 15. Find a solution to the recurrence relation: 2 , 3 0 1 = = - a na a n n a. ! 3 n a n n × = b. ! 3 2 n a n n × × = c. n a n n × × = 3 2 d. n n a 3 2 × = 16. The Math Department has 4 committees that meet once a month. How many different meeting times must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are: C1 = {Allen, Brooks, Marg}, C2 = {Brooks, Jones, Morton}, C3 = {Allen, Marg, Morton}, C4 = {Jones, Marg, Morton}, C5 = {Allen, Brooks}, C6 = {Brooks, Marg, Morton}? a. 2 b. 3 c. 4 d. 5 17. A connected planar graph has 28 edges. If a planar representation of this graph divides the plane into 16 regions, how many vertices does the graph have? a. 14 b. 12 c. 10 d. None of the above 18. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) Î R if and only if x = 1. a. reflexive b. symmetric c. antisymmetric d. transitive 19. Find the Boolean product of the two matrices: ú ú ú û ù ê ê ê ë é × ú ú ú û ù ê ê ê ë é 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 a. ú ú ú û ù ê ê ê ë é 1 1 1 1 1 1 0 1 0 b. ú ú ú û ù ê ê ê ë é 0 1 0 1 1 1 1 1 0 c. ú ú ú û ù ê ê ê ë é 1 1 1 1 1 1 1 1 1 d. ú ú ú û ù ê ê ê ë é 0 0 1 1 1 0 0 1 0 20. True or False? The following relation is an equivalence relation: {(0,1),(1,1),(2,1),(3,3)}. a. True b. False _1388747986.unknown _1389538205.unknown _1389538750.unknown _1389539085.unknown _1389539095.unknown _1389538709.unknown _1389537836.unknown _1389538084.unknown _1388748269.unknown _1388748327.unknown _1388748340.unknown _1388748300.unknown _1388748164.unknown _1388745505.unknown _1388745550.unknown _1388745571.unknown _1388745516.unknown _1388743035.unknown _1388745342.unknown _1388739743.unknown