Csci 2610, Fall 2008 Practice Exam 4 2008.12.03 Name: _ Seat:_
Practice Exam 4 has 13 questions worth a total of 100 points. Please make certain you have all three pages. You will have 75 minutes to complete the exam. Unless otherwise instructed, give all
HW2 solution
3
1. We prove it by contradiction, therefore we assume that 2 is rational. Therefore there are two
3
integers a and b (b 0, with no common factor so that2 = /.
By cubing both sides we get:
2 = 3 / 3
So we know that 3 = 2 3 and because b and t
HW3 solution
1. Examples of one to one and onto
2. S = cfw_-1, 0, 2, 4, 7
a. F(x) = 1 => f(S) = cfw_ 1
b. F(x)= 2x+1 => f(S) = cfw_-1 , 1, 5, 9 , 15
c. F(S) = cfw_ -1, 0, 1
d. cfw_0 , 1, 5, 16
3. Find f inverse : first you have to restrict the domain , in
Quiz 2 :
1.
Total number of digits : 10 x 10 x 10 x 10
a. Digits containing 4 of the same digits like 0000,1111,2222,.,9999 so they are 10
numbers, and the numbers that dont contain 4 repeated digits are :
10 x 10 x 10 x 10 10 = 9990
b. Beginning with odd
1. True or False
a) There are 1000 different 5 digit numbers starting with 32
_T_
b) The number of subsets of S = cfw_1,2,3,.,12 that contain exactly
five elements including 7 or 9 but not both is 2C(10,4)
_F_
c) the number of permutations of the letters
1. True or False
a) There are 1000 different 5 digit numbers starting with 32
_
b) The number of subsets of S = cfw_1,2,3,.,12 that contain exactly
five elements including 7 or 9 but not both is 2C(10,4)
_
c) the number of permutations of the letters in t
1. 1000 to 9999 :
a. 9999/9- 1000/9 = 1000
b. 9999/2 1000/2 = 4500
c. 9 x 9 x 8 x 7
d. 3 :
First divisible by 3 :
9999
1000
- 3
3
= 3000
Total numbers : 9000, 9000-3000 = 6000 not divisible by 3
e. Divisible by either 5, or 7 :
9999
1000
- 5
5
9999
100
Propositional Logic
Proposition: declarative sentence that is either true or false
Tautology: always true
Contradiction: always false
Logically equivilant: two + compound propositions that always have the
same truth values
Conditional Statement (if p then
Csci 2610, Fall 2008 Final Exam 2008.12.16 Name: _ Seat:_
The Final Exam has 14 questions worth a total of 100 points. Please make certain you have all 8 pages. You will have 180 minutes to complete the exam. You are allowed a two-sided sheet of paper wit
Csci 2610, Fall 2008 Exam 2 2008.10.08 Name: _ Seat:_
Exam 2 has 10 questions worth a total of 75 points. Please make certain you have all 4 pages. You will have 50 minutes to complete the exam. 1. (5 points) Given sets A = cfw_1, 2, 3, 4 and B = cfw_3, 4
Csci 2610, Fall 2008 Exam 1 2008.09.10 Name: _ Seat:_
Exam 1 has 9 questions worth a total of 75 points. Please make certain you have all 4 pages. You will have 50 minutes to complete the exam. 1. (5 points) In one sentence, define a proposition.
2.
(10 p
HW1 Solution:
Each of the questions have 10 points and below are point distribution:
Question
Points
1 (a,b,c)
3.3 each part / overall 10
2 (a,b,c,d each part 3 operations)
0.8 each part / overall 10
3
10
4
10
5 (a,b each 5 points)
10
6 (a,b,c,d)
2.5 poin