Question
Please answer the question below.
Select the contrapositive of: If it snows tonight, then I will stay at home. If i stay at home, then it will snow tonight. If I do not stay at home, then I will not snow tonight. If it does not snow tonight, then I will not stay at home. none of the above. Select the correct interpretations (may be more than one) of the notation P(x) is true for all x P(x) is true for at least one x There is no x for which P(x) is true d. There is an x such that P(x) is true Let Q(x) he the statement, "x - 1 1. the first six Fibonacci numbers are: 1. 2, 3, 5, 8, 13. What is the next Fibonacci number? 19 21 23 25 Find f(t) if f is defined recursively by: f(0) -f(1) - 1 and f(n) = f(n - 1)2+f(n-2)2 for n > 1. 5 25 33 1214 Find the sequence (or the recursive formula: sn = - sn-1 + 9, s0 = -3 14, -4 14 -4 6, 14, 86,734 -3,12,-3,12 -3,9, -3., 9 How many different license plates can be created with 7 numbers if any digit is allowed? 604.800 10,000,000 282,475,249 823,543 Find the value of C(16, 6). 8,008 924 5,765,760 12,870 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? 4242 126 931 1131 True of False? an = 2 is a solution to the recurrence relation an = 2an-1 an-2 with initial conditions a0 = 2 and a1, = 2 True False If yon deposit S10,000 in an account that yields 5% interest compounded yearly, what will be the balance at the end of 5 years? $12,625 $13,382 $12,763 $14,186 Find a solution to the recurrence relation: an = an =3n . n! an = 2.3n.n! an = 2.3n.n! an = 2.3n The Math Department has 6 committees that meet once a month. What is the minimum amount of different meeting times that 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: Cl = [Allen, Brooks, Marg}., C2 = [Brooks, Jones, Morion). C3 = {Allen, Marg, Morion}. C4 = {.Tones, Marg, Morton}, C5 = {Allen, Brooks}. C6 = (Brooks, Marg, Morton}? 3 4 5 6 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? 14 12 10 None of the above Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) e R if and only if x = 1. reflexive symmetric antisymmetric transitive Find the Boolean product of the two matrices:[0 1 1 1 1 0 0 1 0].[0 0 1 1 1 1 0 1 1] [0 1 1 1 1 1 0 1 1] [0 1 0 1 1 1 1 1 0] [1 1 1 1 1 1 1 1 1][0 0 1 1 1 0 0 1 0] True or false? The following relation is an equivalence relation: {(0,1);(1; 1 )(2,1 ),(3,3)}. True False
Explanation / Answer
1) Contraposite of P=>Q is not(Q) => not(P), so b)
2) For all x we have P(x), so it implies a) , b) and d) (but definition is a))
3) true for all positive integers, so a)
4) a) and c)
5) d) since 3 and 19 are primes
6) d) since 16=5(mod 11)
7) b) since 8+13=21
8) f(4)=33 by doing it iteratively, so c)
9) s(1)=-(-3)+9=12, so c) by deduction
10) 10^7 , so b)
11) C(16,6)=16!/(10!*6!)=8008, so a)
12) 1,2,3 or 4 C(6,1)C(8,3)+C(6,2)C(8,2)+C(6,3)C(8,1)+C(6,4) = 931, so c)
13) True 2 = 2*2-2 and a0=a1=2
14) 10000*1.05^5 = 12762.81 => c) (rounded)
15) a(n)=2*3^n*n! by immediate induction, so b)
16) The minimal number is the chromatic number of graph, 5 here, so c)
17)v-e+f=2 so v=2-f+e=2-16+28, so v=14 , so a)
18) Is refexive so a)
19) After multiplication we find d) (Using 0+0=0 and 0+1=1+0=1 and 1+1=0)
20) Not reflexive because (0,0) isn't here